Question

Angles Q and R 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​

Answer 1

Answer:

option (ii) is correct.

Step-by-step explanation:

In ΔPQR,

∠PQR+∠QRP+∠RPQ=180  

 [By Angle sum property of a Δ]

⇒25  

+65  

+∠RPQ=180  

⇒90  

+∠RPQ=180  

⇒RPQ=180  

−90  

=90  

Thus, ΔPQR is a right angled triangle, right angled at P,

Side QR is opposite to right angle P

hence QR is hypotenuse

∴[Hypotenuse]  

2

=(Base)  

2

+(Perpendicular)2  [By Pythagoras theorem]

⇒(QR)  

2

=(PR)  

2

+(QP)  

2

Hence, option (ii) is correct.

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