Q6 of 53 Page 153

m∠B = 90 in ΔABC. is altitude to .

If AM = BM = 8, find AC.

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Applying Pythagoras theorem in ΔABM


AB2 = AM2 + BM2


⇒ AB2 = 64 + 64 = 128


Let CM = x


Applying Pythagoras theorem in ΔCBM


⇒ BC2 = BM2 + CM2


⇒ BC2 = x2 + 64


Applying Pythagoras theorem in ΔABC


AC2 = AB2 + BC2


(x + 8)2 = x2 + 64 + 128


⇒ x2 + 64 + 16x = x2 + 192


⇒ 16x = 128


⇒ x = 8 units


AC = AM + CM = 16 units


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