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EmSAT Achieve Exam  >  EmSAT Achieve Tests  >  Mathematics for EmSAT Achieve  >  Case Based Questions Test: Triangles - 1 - EmSAT Achieve MCQ

Case Based Questions Test: Triangles - 1 - EmSAT Achieve MCQ


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15 Questions MCQ Test Mathematics for EmSAT Achieve - Case Based Questions Test: Triangles - 1

Case Based Questions Test: Triangles - 1 for EmSAT Achieve 2024 is part of Mathematics for EmSAT Achieve preparation. The Case Based Questions Test: Triangles - 1 questions and answers have been prepared according to the EmSAT Achieve exam syllabus.The Case Based Questions Test: Triangles - 1 MCQs are made for EmSAT Achieve 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Case Based Questions Test: Triangles - 1 below.
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Case Based Questions Test: Triangles - 1 - Question 1
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Direction: Read the following text and answer the below questions:
SCALE FACTOR
A scale drawing of an object is the same shape at the object but a different size. The scale of a drawing is a comparison of the length used on a drawing to the length it represents. The scale is written as a ratio. The ratio of two corresponding sides in similar figures is called the scale factor
Scale factor = length in image / corresponding length in object

If one shape can become another using revising, then the shapes are similar. Hence, two shapes are similar when one can become the other after a resize, flip, slide or turn. In the photograph below showing the side view of a train engine. Scale factor is 1:200
This means that a length of 1 cm on the photograph above corresponds to a length of 200 cm or 2 m, of the actual engine. The scale can also be written as the ratio of two lengths.
The length of AB in the given figure:

Detailed Solution for Case Based Questions Test: Triangles - 1 - Question 1

Since, ΔABC and ΔADE are similar, then their ratio of corresponding sides are equal.

6x = 3(x + 4)

6x = 3x + 12

6x – 3x = 12

3x = 12 x = 4

Hence, AB = 4 cm.

Case Based Questions Test: Triangles - 1 - Question 2
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Direction: Read the following text and answer the below questions:

SCALE FACTOR

A scale drawing of an object is the same shape at the object but a different size. The scale of a drawing is a comparison of the length used on a drawing to the length it represents. The scale is written as a ratio. The ratio of two corresponding sides in similar figures is called the scale factor

Scale factor = length in image / corresponding length in object

If one shape can become another using revising, then the shapes are similar. Hence, two shapes are similar when one can become the other after a resize, flip, slide or turn. In the photograph below showing the side view of a train engine. Scale factor is 1:200

This means that a length of 1 cm on the photograph above corresponds to a length of 200 cm or 2 m, of the actual engine. The scale can also be written as the ratio of two lengths.

What will affect the similarity of any two polygons?

Detailed Solution for Case Based Questions Test: Triangles - 1 - Question 2
The common way of defining the Similarity of polygons is

Any two polygons are said to be similar if they are of the same shape and they can be of different sizes.

The Mathematical definition is, Any two polygons are said to be similar if they satisfy the below two conditions.

  • The corresponding sides of both the polygons are in the same proportion.

  • The corresponding interior angles of the polygons are the same.

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Case Based Questions Test: Triangles - 1 - Question 3
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Direction: Read the following text and answer the below questions:

SCALE FACTOR

A scale drawing of an object is the same shape at the object but a different size. The scale of a drawing is a comparison of the length used on a drawing to the length it represents. The scale is written as a ratio. The ratio of two corresponding sides in similar figures is called the scale factor

Scale factor = length in image / corresponding length in object

If one shape can become another using revising, then the shapes are similar. Hence, two shapes are similar when one can become the other after a resize, flip, slide or turn. In the photograph below showing the side view of a train engine. Scale factor is 1:200

This means that a length of 1 cm on the photograph above corresponds to a length of 200 cm or 2 m, of the actual engine. The scale can also be written as the ratio of two lengths.

If two similar triangles have a scale factor 5:3 which statement regarding the two triangles is true?

Detailed Solution for Case Based Questions Test: Triangles - 1 - Question 3
25:15= 25/15 = 5/3.

As 5 divides both. ( i. e., 5 x 5 = 25, 5 x 3 = 15)

Case Based Questions Test: Triangles - 1 - Question 4
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Direction: Read the following text and answer the below questions:

SCALE FACTOR

A scale drawing of an object is the same shape at the object but a different size. The scale of a drawing is a comparison of the length used on a drawing to the length it represents. The scale is written as a ratio. The ratio of two corresponding sides in similar figures is called the scale factor

Scale factor = length in image / corresponding length in object

If one shape can become another using revising, then the shapes are similar. Hence, two shapes are similar when one can become the other after a resize, flip, slide or turn. In the photograph below showing the side view of a train engine. Scale factor is 1:200

This means that a length of 1 cm on the photograph above corresponds to a length of 200 cm or 2 m, of the actual engine. The scale can also be written as the ratio of two lengths.

If the length of the model is 11 cm, then the overall length of the engine in the photograph above, including the couplings(mechanism used to connect) is:
Detailed Solution for Case Based Questions Test: Triangles - 1 - Question 4

Given that

Scale factor is 1:200

Therefore,

11 x 200 cm = Length of real life engine

2200 cm = Length of real life engine

Length of real life engine = 2200 cm

Length of real life engine

Length of real life engine = 22 m.

Case Based Questions Test: Triangles - 1 - Question 5
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Direction: Read the following text and answer the below questions:

SCALE FACTOR

A scale drawing of an object is the same shape at the object but a different size. The scale of a drawing is a comparison of the length used on a drawing to the length it represents. The scale is written as a ratio. The ratio of two corresponding sides in similar figures is called the scale factor

Scale factor = length in image / corresponding length in object

If one shape can become another using revising, then the shapes are similar. Hence, two shapes are similar when one can become the other after a resize, flip, slide or turn. In the photograph below showing the side view of a train engine. Scale factor is 1:200

This means that a length of 1 cm on the photograph above corresponds to a length of 200 cm or 2 m, of the actual engine. The scale can also be written as the ratio of two lengths.

What is the actual width of the door if the width of the door in photograph is 0.35 cm?
Detailed Solution for Case Based Questions Test: Triangles - 1 - Question 5
Given that

Scale factor is 1:200

Therefore,

0.35 x 200 cm = Actual width of the door

= Actual width of the door

35 x 2 cm = Actual width of the door

70 cm = Actual width of the door

Actual width of the door = 70 cm

Actual width of the door

Actual width of the door = 0.7 m.

Case Based Questions Test: Triangles - 1 - Question 6
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Direction: Read the following text and answer the below questions:

Seema placed a light bulb at point O on the ceiling and directly below it placed a table. Now, she put a cardboard of shape ABCD between table and lighted bulb. Then a shadow of ABCD is casted on the table as A'B'C'D' (see figure). Quadrilateral A'B'C'D' in an enlargement of ABCD with scale factor 1 : 2, Also, AB = 1.5 cm, BC = 25 cm, CD = 2.4 cm and AD = 2.1 cm; ∠A = 105°, ∠B = 100°, ∠C = 70° and ∠D = 85°.

What is the sum of angles C' and D'?
Detailed Solution for Case Based Questions Test: Triangles - 1 - Question 6
∠C' = ∠C = 70°

and ∠D' = ∠D = 85°

∴ ∠C' + ∠D' = 70° + 85° = 155°

Case Based Questions Test: Triangles - 1 - Question 7
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Direction: Read the following text and answer the below questions:

Seema placed a light bulb at point O on the ceiling and directly below it placed a table. Now, she put a cardboard of shape ABCD between table and lighted bulb. Then a shadow of ABCD is casted on the table as A'B'C'D' (see figure). Quadrilateral A'B'C'D' in an enlargement of ABCD with scale factor 1 : 2, Also, AB = 1.5 cm, BC = 25 cm, CD = 2.4 cm and AD = 2.1 cm; ∠A = 105°, ∠B = 100°, ∠C = 70° and ∠D = 85°.

What is the length of A'B' ?
Detailed Solution for Case Based Questions Test: Triangles - 1 - Question 7
Given scale factor is 1 : 2

∴ A'B' = 2AB

⇒ A'B' = 2 × 1.5 = 3 cm

Case Based Questions Test: Triangles - 1 - Question 8
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Direction: Read the following text and answer the below questions:

Seema placed a light bulb at point O on the ceiling and directly below it placed a table. Now, she put a cardboard of shape ABCD between table and lighted bulb. Then a shadow of ABCD is casted on the table as A'B'C'D' (see figure). Quadrilateral A'B'C'D' in an enlargement of ABCD with scale factor 1 : 2, Also, AB = 1.5 cm, BC = 25 cm, CD = 2.4 cm and AD = 2.1 cm; ∠A = 105°, ∠B = 100°, ∠C = 70° and ∠D = 85°.

What is the ratio of sides A'B' and A'D' ?
Detailed Solution for Case Based Questions Test: Triangles - 1 - Question 8
A'B' = 3 cm

and A'D' = 2AD

= 2 × 2.1 = 4.2 cm

∴ A'B'/A'D' = 3/4.2 = 30/42

= 5/7 or 5 : 7

Case Based Questions Test: Triangles - 1 - Question 9
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Direction: Read the following text and answer the below questions:

Seema placed a light bulb at point O on the ceiling and directly below it placed a table. Now, she put a cardboard of shape ABCD between table and lighted bulb. Then a shadow of ABCD is casted on the table as A'B'C'D' (see figure). Quadrilateral A'B'C'D' in an enlargement of ABCD with scale factor 1 : 2, Also, AB = 1.5 cm, BC = 25 cm, CD = 2.4 cm and AD = 2.1 cm; ∠A = 105°, ∠B = 100°, ∠C = 70° and ∠D = 85°.

What is the measurement of angle A' ?
Detailed Solution for Case Based Questions Test: Triangles - 1 - Question 9
Quadrilateral A'B'C'D' is similar to ABCD.

∴ ∠A' = ∠A

⇒ ∠A' = 105°

Case Based Questions Test: Triangles - 1 - Question 10
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Direction: Read the following text and answer the below questions:

Seema placed a light bulb at point O on the ceiling and directly below it placed a table. Now, she put a cardboard of shape ABCD between table and lighted bulb. Then a shadow of ABCD is casted on the table as A'B'C'D' (see figure). Quadrilateral A'B'C'D' in an enlargement of ABCD with scale factor 1 : 2, Also, AB = 1.5 cm, BC = 25 cm, CD = 2.4 cm and AD = 2.1 cm; ∠A = 105°, ∠B = 100°, ∠C = 70° and ∠D = 85°.

What is the sum of angles of quadrilateral A'B'C'D' ?
Detailed Solution for Case Based Questions Test: Triangles - 1 - Question 10
Sum of the angles of quadrilateral A'B'C'D' is 360°
Case Based Questions Test: Triangles - 1 - Question 11
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Direction: Read the following text and answer the below questions:

Rohan wants to measure the distance of a pond during the visit to his native. He marks points A and B on the opposite edges of a pond as shown in the figure below.

To find the distance between the points, he makes a right-angled triangle using rope connecting B with another point C are a distance of 12 m, connecting C to point D at a distance of 40 m from point C and the connecting D to the point A which is are a distance of 30 m from D such the ∠ADC = 90°.

Find the length of the rope used.
Detailed Solution for Case Based Questions Test: Triangles - 1 - Question 11
Length of Rope = BC + CD + DA

= 12 m + 40 m + 30 m

= 82 m

Case Based Questions Test: Triangles - 1 - Question 12
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Direction: Read the following text and answer the below questions:

Rohan wants to measure the distance of a pond during the visit to his native. He marks points A and B on the opposite edges of a pond as shown in the figure below.

To find the distance between the points, he makes a right-angled triangle using rope connecting B with another point C are a distance of 12 m, connecting C to point D at a distance of 40 m from point C and the connecting D to the point A which is are a distance of 30 m from D such the ∠ADC = 90°.

What is the distance AC?
Detailed Solution for Case Based Questions Test: Triangles - 1 - Question 12
According to the pythagoras,

AC2 = AD2 + CD2

AC2 = (30 m)2 + (40 m)2

AC2 = 900 + 1600

AC2 = 2500

AC = 50 m

Case Based Questions Test: Triangles - 1 - Question 13
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Direction: Read the following text and answer the below questions:

Rohan wants to measure the distance of a pond during the visit to his native. He marks points A and B on the opposite edges of a pond as shown in the figure below.

To find the distance between the points, he makes a right-angled triangle using rope connecting B with another point C are a distance of 12 m, connecting C to point D at a distance of 40 m from point C and the connecting D to the point A which is are a distance of 30 m from D such the ∠ADC = 90°.

Find the length AB?
Detailed Solution for Case Based Questions Test: Triangles - 1 - Question 13
AC = 50 m

BC = 12 m

AC = AB + BC

50 m = AB + 12 m

AB = 50 m – 12 m

AB = 38 m

Case Based Questions Test: Triangles - 1 - Question 14
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Direction: Read the following text and answer the below questions:

Rohan wants to measure the distance of a pond during the visit to his native. He marks points A and B on the opposite edges of a pond as shown in the figure below.

To find the distance between the points, he makes a right-angled triangle using rope connecting B with another point C are a distance of 12 m, connecting C to point D at a distance of 40 m from point C and the connecting D to the point A which is are a distance of 30 m from D such the ∠ADC = 90°.

Which property of geometry will be used to find the distance AC?
Detailed Solution for Case Based Questions Test: Triangles - 1 - Question 14
In △ADC

We know two sides AD, CD

And, we find AC using Pythagoras Theorem.

Case Based Questions Test: Triangles - 1 - Question 15
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Direction: Read the following text and answer the below questions:

Rohan wants to measure the distance of a pond during the visit to his native. He marks points A and B on the opposite edges of a pond as shown in the figure below.

To find the distance between the points, he makes a right-angled triangle using rope connecting B with another point C are a distance of 12 m, connecting C to point D at a distance of 40 m from point C and the connecting D to the point A which is are a distance of 30 m from D such the ∠ADC = 90°.

Which is the following does not form a Pythagoras triplet?
Detailed Solution for Case Based Questions Test: Triangles - 1 - Question 15
We need to check each and every option

Option A - (7, 24, 25)

72 + 242 = 49 + 576

= 625

= 252

So, this is a Pythagorean triplet

Option B - (15, 8, 17)

152 + 82 = 225 + 64

= 289

= 172

So, this is a Pythagorean triplet

Option C - (5, 12, 13)

52 + 122 = 25 + 144

= 169

= 132

So, this is a Pythagorean triplet

Option D - (21, 20, 28)

212 + 202 = 441 + 400

= 881

≠ 282

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