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Olympiad Test: The Triangle and Its Properties - Class 7 MCQ


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20 Questions MCQ Test Mathematics (Maths) Class 7 - Olympiad Test: The Triangle and Its Properties

Olympiad Test: The Triangle and Its Properties for Class 7 2024 is part of Mathematics (Maths) Class 7 preparation. The Olympiad Test: The Triangle and Its Properties questions and answers have been prepared according to the Class 7 exam syllabus.The Olympiad Test: The Triangle and Its Properties MCQs are made for Class 7 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Olympiad Test: The Triangle and Its Properties below.
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Olympiad Test: The Triangle and Its Properties - Question 1

A In a ΔABC, if AB2=BC2+AC2,at which vertex is the right angle?

Detailed Solution for Olympiad Test: The Triangle and Its Properties - Question 1

AB is the hypotenuse ⇒ C has the right angle.

Olympiad Test: The Triangle and Its Properties - Question 2

Which type of triangle is formed by BC=7.2cm, AC=6 cm and ∠120o?

Detailed Solution for Olympiad Test: The Triangle and Its Properties - Question 2

Since ∠C=120o>90o, the triangle formed is obtuse.

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Olympiad Test: The Triangle and Its Properties - Question 3

In the Pythagoras property, the triangle must be ___________ .

Olympiad Test: The Triangle and Its Properties - Question 4

Find the value of x in this figure.

Detailed Solution for Olympiad Test: The Triangle and Its Properties - Question 4

x + x+ x = 180 degrees [ angle sum property ]
3x = 180
x = 180/3 

x= 60 degree 

Olympiad Test: The Triangle and Its Properties - Question 5

Find the value of x in given figure.

Detailed Solution for Olympiad Test: The Triangle and Its Properties - Question 5

Exterior angle is equal to sum of interior opposite angles so,
120 = 60+x
x = 60°

Olympiad Test: The Triangle and Its Properties - Question 6

In ΔPQR, PD is

Detailed Solution for Olympiad Test: The Triangle and Its Properties - Question 6

Median is a line joining the vertex and middle of the opposite side, and hence dividing the triangle in two equal parts. So PD is the median.

Olympiad Test: The Triangle and Its Properties - Question 7

The value of x in the adjoining figure is 

Detailed Solution for Olympiad Test: The Triangle and Its Properties - Question 7


y + 125 = 180 
y = 55
and x+ y + 90 = 180
  x + 55 + 90 = 180 
x = 35

Olympiad Test: The Triangle and Its Properties - Question 8

If the two legs of a right angled triangle are equal and the square of the hypotenuse is 100 sq units, what is the length of each leg?

Detailed Solution for Olympiad Test: The Triangle and Its Properties - Question 8

Let's solve the problem step by step:

Given:

  • The two legs of a right-angled triangle are equal.
  • The square of the hypotenuse is 100 square units.

Let the length of each leg be x units.

Using the Pythagorean theorem:

 

Olympiad Test: The Triangle and Its Properties - Question 9

Find the value of unknown x in the adjoining figure.

Detailed Solution for Olympiad Test: The Triangle and Its Properties - Question 9

x + 50 + 60 = 180
x + 110 = 180
x = 70

Olympiad Test: The Triangle and Its Properties - Question 10

What is the measure of angle x ?

Detailed Solution for Olympiad Test: The Triangle and Its Properties - Question 10

if in a triangle 2 sides are equal then the angles would also be equal
x = 40ο

Olympiad Test: The Triangle and Its Properties - Question 11

ΔABC is right-angled at C. If AC = 5 cm and BC = 12 cm find the length of AB.

Detailed Solution for Olympiad Test: The Triangle and Its Properties - Question 11

AB2=AC2+BC2=52+122=25+144 = 169
AB=13 cm

Olympiad Test: The Triangle and Its Properties - Question 12

ΔPQR is a triangle right-angled at P. If PQ = 3 cm and PR = 4 cm, find QR.

Detailed Solution for Olympiad Test: The Triangle and Its Properties - Question 12

Using pythagoras theorem,
QR= PR+ PQ2
42+32
=16+9=25
QR = 5cm

Olympiad Test: The Triangle and Its Properties - Question 13

Which is the longest side in the triangle PQR right angled at P?

Detailed Solution for Olympiad Test: The Triangle and Its Properties - Question 13

In a triangle, the side which is opposite to largest angle is the longest side.

Now, In a right - angled triangle, largest angle is always 90.

So, the side which is opposite to 90 is longest side.

Since, the side opposite to right - angle is known as "Hypotenuse".

Hypotenuse of a triangle is the longest side of a triangle.


In ΔPQR, if ∠P=90∘ then QR is the longest side.

Hence, QR is the longest side.

Olympiad Test: The Triangle and Its Properties - Question 14

Which is the longest side in the triangle ABC right angled at B?

Olympiad Test: The Triangle and Its Properties - Question 15

Which is the longest side of a right triangle?

Olympiad Test: The Triangle and Its Properties - Question 16

What is the measure of angles x?

Detailed Solution for Olympiad Test: The Triangle and Its Properties - Question 16

Since the two sides are equal, the angles opposite to them are also equal. So x+45° + 45° = 180°, x = 90°

Olympiad Test: The Triangle and Its Properties - Question 17

The value of x in the adjoining figure is

Detailed Solution for Olympiad Test: The Triangle and Its Properties - Question 17

as two sides are equal so it is a isoceles triangle with one angle as 90° so other remaining two will be
each 45° 

Olympiad Test: The Triangle and Its Properties - Question 18

A triangle in which all three sides are of equal lengths is called _________.

Olympiad Test: The Triangle and Its Properties - Question 19

If the angles of a triangle are in the ratio 1:2:7,what type of a triangle is it?

Detailed Solution for Olympiad Test: The Triangle and Its Properties - Question 19

 Let the measures of the angles be 1x,2x and 7x. We have, 1x+2x+7x=180o⇒ x=18o The angles are 18o,36o and 126o.
∴ The triangle is obtuse angled.

Olympiad Test: The Triangle and Its Properties - Question 20

Two chimneys 18m and 13m high stand upright on a ground. If their feet are 12m apart, what is the distance between their tops?

Detailed Solution for Olympiad Test: The Triangle and Its Properties - Question 20

Since the two sides are equal, the angles opposite to them are also equal to the adjacent angle of 120° which is equal to 180° - 120° =60° is equal to x. So x = 60°

To find the distance between the tops of chimneys, we have to find AC. By Pythagoras' theorem,
AC2=AB2+BC2 (Since ΔABC is a right triangle.) ⇒ AC2=52+122=169 ⇒ AC==13m

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