Q3 of 53 Page 153

In ΔPQR, is the altitude to hypotenuse ? If PM = 8, RM = 12, find PQ, QR and QM.

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m∠Q = 90


RM = 12


MP = 8


∴ RP = (RM + MP) = 20


Let QM be x


Applying Pythagoras theorem in ΔQMP, we get


QP2 = x2 + 82 = x2 + 64


Applying Pythagoras theorem in ΔQMR, we get


QR2 = x2 + 122 = x2 + 144


Applying Pythagoras theorem in ΔPQR, we get


RP2 = (x2 + 64) + (x2 + 144)


⇒ 400 = 208 + 2x2


⇒ x2 = 96


⇒ x = 4√6


⇒ QM = 4√6


PQ2 = x2 + 64


⇒ PQ2 = 160


⇒ PQ = 4√10


QR2 = x2 + 144


⇒ QR2 = 240


⇒ QR = 4√15


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