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

The Triangle and its Properties

Question 1.
PQR is a triangle, right-angled at P. If PQ = 10 cm and PR? = 24 cm, find QR.

Solution:

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties 21
NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties 22

Question 2.
ABC is a triangle right-angled atC. If AB = 25 cm and AC = 7cm, find BC.

Solution:

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties 23

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.
NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties 24
Solution:
NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties 25
Hence, the distance of the foot of the ladder from the wall is 9 m.

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:

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties 26
NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties 27

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

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 be the tree before it broke at the point C. and let its top A touch the ground at A after it broke. Then, ∆ABC is a right triangle, right-angled at B such that A’ B = 12 m, BC = 5 m. By Pythagoras theorem, we have
NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties 29

Question 6.
Angles Q and ii of a APQR are 25° and 65°. Write which of the following is true :
(i)
 PQ2 + QR2 = RP2
(ii) PQ2 + RP2 = QR2
(iii) RP2 + QR2 = PQ2

Solution:

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties 31

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 BC2 = AC2 – AB2

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.
NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties 33

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