CBSE students can refer to NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.5 Textbook Questions and Answers are provided by experts in order to help students secure good marks in exams.

## Class 7 Maths NCERT Solutions Chapter 6 The Triangle and its Properties Ex 6.5

**Ex 6.5 Class 7 Maths Question 1.**

PQR is a triangle, right-angled at P. If PQ = 10 cm and PR = 24 cm, find QR?

**Solution:
**

**Ex 6.5 Class 7 Maths Question 2.**

ABC is a triangle right-angled atC. If AB = 25 cm and AC = 7cm, find BC?

**Solution:
**

**Ex 6.5 Class 7 Maths Question 3.**

A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.

**Solution:**

Hence, the distance of the foot of the ladder from the wall is 9 m.

**Ex 6.5 Class 7 Maths Question 4.**

Which of the following can be the sides of a right triangle?

**(i)** 2.5 em, 6.5 cm, 6 cm.

**(ii)** 2 cm, 2 cm, 5 cm.

**(iii)** 1.5 cm, 2 cm, 2.5 cm.

In the case of right-angled triangles, identify the right angles.

**Solution:
**

Thus, the given sides form a right triangle and the right-angle is opposite to the side of length 2.5 cm.

**Ex 6.5 Class 7 Maths Question 5.**

A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.

**Solution:
**

Let ACB by the tree before it broke at point C. and let its top Touch the ground at A after it broke. Then, ∆AABC is a right triangle, right-angled at B such that A’ B = 12 m, BC = 5 m.

By Pythagoras theorem, we have

**Ex 6.5 Class 7 Maths Question 6.**

Angles Q and ii of an APQR are 25° and 65°. Write which of the following is true:

**(i)** PQ^{2} + QR^{2} = RP^{2}

**(ii)** PQ^{2} + RP^{2} = QR^{2}

**(iii)** RP^{2} + QR^{2} = PQ^{2
}

**Solution:
**

**Ex 6.5 Class 7 Maths Question 7.**

Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.

**Solution:**

Let ABCD be a rectangle such that AB = 40 m and AC = 41 m.

In right-angled ∆ABC, right-angled at B, by Pythagoras theorem, we have BC^{2} = AC^{2} – AB^{2
}

**Ex 6.5 Class 7 Maths Question 8.**

The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.

**Solution:**

Let ABCD be the rhombus such that AC = 30 cm and BD = 16 cm.

We know that the diagonals of a rhombus bisect each other at right angles.

We hope the NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties help you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties, drop a comment below and we will get back to you at the earliest.