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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

6. Angles Q and R of a  \small \Delta PQR  are  \small 25^{\circ}  and  \small 65^{\circ}. Write which of the following is true:

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

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

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

        

Answers (1)
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As we know the sum of the angles of any triangle is always 180. So,

\angle P + \angle Q + \angle R = 180^0

\angle P + 25^0 + 65^0 = 180^0

\angle P = 180^0- 25^0 - 65^0

\angle P = 90^0

Now. Since PQR is a right-angled triangle with right angle at P. So

(Hypotenus)^2=(Base)^2+(Perpendicular)^2

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

 \small PQ^2+RP^2=QR^2

Hence option (ii) is correct.

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