Table of Contents

Toggle## Class 7, Maths, Chapter 6, Exercise 6.5 Solutions

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

**Q.2. ABC is a triangle, right-angled at C. If AB = 25 cm and AC = 7 cm, find BC.**

**Q.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.**

**Q.4. Which of the following can be the sides of a right triangle?**

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

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

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

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

**Ans:**

**(i)**** Let a = 2.5 cm, b = 6.5 cm, c = 6 cm**

Let the largest value is the hypotenuse side

i.e. b = 6.5 cm. by Pythagoras theorem,

**(Hypotenuse) ^{2} = (Base)^{2} + (Perpendicular)^{2}**

⟹ (b)^{2} = (a)^{2} + (c)^{2}

⟹ (6.5)^{2} = (2.5)^{2} + (6)^{2}

⟹ (6.5 x 6.5 ) = (2.5 x 2.5 ) + (6 x 6)

⟹ 42.25 = 6.25 + 36

⟹ 42.25 = 42.25

⟹ LHS = RHS

The sum of square of two side of triangle is equal to the square of third side,

∴The given triangle is right-angled triangle.

Right angle lies on the opposite of the greater side 6.5 cm.

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

Let the largest value is the hypotenuse side i.e. c = 5 cm.

by Pythagoras theorem,**(Hypotenuse) ^{2} = (Base)^{2} + (Perpendicular)^{2}**

⟹ (c)^{2} = (a)^{2} + (b)^{2}

⟹ (5)^{2} = (2)^{2} + (2)^{2}

⟹ (5 x 5 ) = (2 x 2 ) + (2 x 2)

⟹ 25 = 4 + 4

⟹ 25 ≠ 8

⟹ LHS ≠ RHS

The sum of square of two side of triangle is not equal to the square of third side,

∴ The given triangle is not right-angled triangle.

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

Let the largest value is the hypotenuse side i.e. c = 2.5 cm.

by Pythagoras theorem,

(Hypotenuse)^{2} = (Base)^{2} + (Perpendicular)^{2}

⟹ (c)^{2} = (a)^{2} + (b)^{2}

⟹ (2.5)^{2} = (1.5)^{2} + (2)^{2}

⟹ (2.5 x 2.5 ) = (1.5 x 1.5 ) + (2 x 2)

⟹ 6.25 = 2.25 + 4

⟹ 6.25 = 6.25

⟹ LHS = RHS

The sum of square of two side of triangle is equal to the square of third side,

∴The given triangle is right-angled triangle. Right angle lies on the opposite of the greater side 2.5 cm.

**Q.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.**

**Ans:**

Let TCB is the tree and after broken at point C, the top of Tree ‘T’ touches the ground at ‘A’ from the base of tree at a distance of AB = 12 m.

The, ΔABC is a right angled triangle in which AB = 12 m, BC = 5m and right angled at B.

**Q.6. Angles Q and R of a ∆PQR are 25º and 65º. 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}**

**Q.7. Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.**

**Q.8. The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.**

## NCERT Solutions For Class 7 Maths, Chapter 6, The Triangle and its Properties (All Exercises)

**Class 7, Maths, Chapter 6, The Triangle and Its Properties **

**Class 7, Maths, Chapter 6, The Triangle and Its Properties, Exercise 6.1**

**Class 7, Maths, Chapter 6, The Triangle and Its Properties, Exercise 6.2**

**Class 7, Maths, Chapter 6, The Triangle and Its Properties, Exercise 6.3**

**Class 7, Maths, Chapter 6, The Triangle and Its Properties, Exercise 6.4 **

**Class 7, Maths, Chapter 6, The Triangle and Its Properties, Exercise 6.5** **← You are here**