(i) \( PQ^2 + QR^2 = RP^2 \)

(ii)\( PQ^2 + RP^2 = QR^2 \)

(iii)\( RP^2 + QR^2 = PQ^2 \)

Answer :

We know that

\(\angle P + \angle Q + \angle R = 180° \)(Angle sum property)

\(\angle \)P + 25° + 65° = 180°

\(\angle \)P + 90° = 180°

\(\angle \)P = 180° – 90° – 90°

\(\triangle \)PQR is a right triangle, right angled at P

(i) Not True

\(\therefore PQ^2 + QR^2 \neq RP^2 \) (By Pythagoras property)

(ii) True

\(\therefore \) \(PQ^2 + RP^2 = QP^2 \) (By Pythagoras property)

(iii) Not True

\(\therefore RP^2 + QR^2 \neq PQ^2 \)(By Pythagoras property)

- 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, 2 cm, 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.
- 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 1 Integers
- NCERT solutions for class 7 maths chapter 2 Fractions and Decimals
- NCERT solutions for class 7 maths chapter 3 Data Handling
- NCERT solutions for class 7 maths chapter 4 Simple Equations
- NCERT solutions for class 7 maths chapter 5 Lines and Angles
- NCERT solutions for class 7 maths chapter 6 The Triangle and its Properties
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- NCERT solutions for class 7 maths chapter 9 Rational Numbers
- NCERT solutions for class 7 maths chapter 10 Practical Geometry
- NCERT solutions for class 7 maths chapter 11 Perimeter and Area
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- NCERT solutions for class 7 maths chapter 13 Exponents and Powers
- NCERT solutions for class 7 maths chapter 14 Symmetry
- NCERT solutions for class 7 maths chapter 15 Visualising Solid Shapes

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- NCERT solutions for class 7 science chapter 2 Nutrition In Animals
- NCERT solutions for class 7 science chapter 3 Fibre to Fabric
- NCERT solutions for class 7 science chapter 4 Heat
- NCERT solutions for class 7 science chapter 5 Acids Bases and Salts
- NCERT solutions for class 7 science chapter 6 Physical and Chemical Changes
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