Worksheet: Triangles

# Triangles Class 10 Worksheet Maths Chapter 6

### Multiple Choice Questions

Q1: Which of the following triangles have the same side lengths?
(a) Scalene
(b) Isosceles
(c) Equilateral
(d) None of these

Q2: Area of an equilateral triangle with side length a is equal to:
(a) (√3/2)a
(b) (√3/2)a2
(c) (√3/4) a2
(d) (√3/4) a

Q3: D and E are the midpoints of side AB and AC of a triangle ABC, respectively, and BC = 6 cm. If DE || BC, then the length (in cm) of DE is:
(a) 2.5
(b) 3
(c) 5
(d) 6
Q4: The diagonals of a rhombus are 16 cm and 12 cm, in length. The side of the rhombus in length is:
(a) 20 cm
(b) 8 cm
(c) 10 cm
(d) 9 cm

Q5: Corresponding sides of two similar triangles are in the ratio of 2:3. If the area of the small triangle is 48 sq.cm, then the area of the large triangle is:
(a) 230 sq.cm.
(b) 106 sq.cm
(c) 107 sq.cm.
(d) 108 sq.cm

Q6: If the perimeter of a triangle is 100 cm and the length of two sides are 30 cm and 40 cm, the length of the third side will be:
(a) 30 cm
(b) 40 cm
(c) 50 cm
(d) 60 cm

Q7: If triangles ABC and DEF are similar and AB = 4 cm, DE = 6 cm, EF = 9 cm, and FD = 12 cm, the perimeter of triangle ABC is:
(a) 22 cm
(b) 20 cm
(c) 21 cm
(d) 18 cm

Q8: The height of an equilateral triangle of side 5 cm is:
(a) 4.33 cm
(b) 3.9 cm
(c) 5 cm
(d) 4 cm

Q9: If ABC and DEF are two triangles and AB/DE = BC/FD, then the two triangles are similar if
(a) ∠A = ∠F
(b) ∠B = ∠D
(c) ∠A = ∠D
(d) ∠B = ∠E

Q10: Sides of two similar triangles are in the ratio 4: 9. Areas of these triangles are in the ratio
(a) 2: 3
(b) 4: 9
(c) 81: 16
(d) 16: 81

### Solve the following Questions

Q1: The areas of two similar triangles ABC and PQR are in the ratio 9 : 16. If BC = 4.5 cm, find the length of QR.

Q2: Determine whether the triangle having sides (b − 1) cm, 2√b cm and (b + 1) cm is a right angled triangle.

Q3: Sides of triangles are given below. Determine which of them are right triangles.In case of a right triangle, write the length of its hypotenuse.
(i) 7 cm, 24 cm, 25 cm
(ii) 3 cm,4 cm,5 cm
(iii) 40 cm, 80 cm, 100 cm
(iv) 13 cm, 12 cm, 5 cm

Q4: In ΔABC, AD is perpendicular to BC. Prove that:
a. AB2 + CD2 = AC2 + BD2
b. AB2 − BD2 = AC2 − CD2

Q5: Triangle ABC is right- angled at B and D is the mid - point of BC.
Prove that: AC= 4AD2 − 3AB2

Q6: ABC is an isosceles triangle, right -angled at C. Prove that AB2 = 2BC2 .

Q7: A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

Q8: The foot of a ladder is 6 m away from a wall and its top reaches a window 8 m above the ground. If the ladder is shifted in such a way that its foot is 8 m away from the wall, to what height does its tip reach?

Q9: The areas of two similar triangles are 121 cm2 and 64 cm2 respectively. If the median of the first triangle is 12.1 cm, find the corresponding median of the other.

Q10: DEF is an equilateral triangle of side 2b. Find each of its altitudes.

The document Triangles Class 10 Worksheet Maths Chapter 6 is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10

## Mathematics (Maths) Class 10

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## FAQs on Triangles Class 10 Worksheet Maths Chapter 6

 1. What are the different types of triangles?
Ans. There are three main types of triangles: equilateral triangles, isosceles triangles, and scalene triangles. An equilateral triangle has all three sides of equal length, an isosceles triangle has two sides of equal length, and a scalene triangle has no sides of equal length.
 2. How do you find the area of a triangle?
Ans. To find the area of a triangle, you can use the formula A = (1/2) * base * height, where the base is the length of the triangle's base and the height is the perpendicular distance from the base to the opposite vertex.
 3. Can a triangle have two right angles?
Ans. No, a triangle cannot have two right angles. The sum of the interior angles in a triangle is always 180 degrees, and if a triangle had two right angles, the sum would be greater than 180 degrees, which is not possible.
 4. How can you determine if three given side lengths form a triangle?
Ans. To determine if three given side lengths form a triangle, you can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. If this condition is satisfied for all three combinations of side lengths, then the given side lengths form a triangle.
 5. What is the Pythagorean theorem and how is it used in triangles?
Ans. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem is used to find the length of a side in a right-angled triangle when the lengths of the other two sides are known.

## Mathematics (Maths) Class 10

116 videos|420 docs|77 tests

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