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

In ∆ PQR,
∠PQR + ∠QRP + ∠RPQ = 180° [By Angle sum property of a ∆ ]
⇒ 25° + 65° + ∠RPQ = 180
⇒ 90° ∠RPQ=180°
⇒ ∠RPQ = 180° – 90° = 90°
Thus, ∆ PQR is a right angled triangle, right angled at P.
∴ (Hypotenuse)² = (Base)² + (Perpendicular)² [By Pythagoras theorem]
⇒ (QR)² = (PR)² + (QP)²
Hence, Option (ii) is correct.

Class 7 Maths Chapter 6 Exercise 6.5

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