Q16 of 27 Page 289

In the adjoining figure, the point O is situated within the triangle PQR in such a way that ∠POQ = 90°, OP = 6cm. and OQ = 8cm. If PR = 24cm. and ∠QPR = 90°, then let us write the length of QR.

Given: PQR and POQ are right angled triangles.


∠QPR = 90°


∠POQ = 90°


OP = 6 cm


OQ = 8 cm


PR = 24 cm


By applying Pythagoras theorem to ΔPOQ, we get,


PQ2 = OP2 + OQ2


⇒ PQ2 = 62 + 82


⇒ PQ2 = 36 + 64


⇒ PQ2 = 100 = 102


⇒ PQ = 10 cm


Now, by applying Pythagoras Theorem to ΔPQR, we get,


QR2 = PQ2 + PR2


⇒ QR2 = 102 + 242


⇒ QR2 = 100 + 576


⇒ QR2 = 676 = 262


⇒ QR = 26 cm


Thus, QR is 26 cm long.


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