Q. 135.0( 1 Vote )

ΔABC is an isosceles triangle with AB = AC = 13 cm. The length of altitude from A on BC is 5 cm. Find BC.

Answer :


Given: ABC is an isosceles triangle with AB = AC = 13 cm


Suppose the altitude from A on Bc meets BC at M.


M is the midpoint of BC. AM = 5 cm


In ∆AMB, using Pythagoras theorem, we have


(Perpendicular)2 + (Base)2 = (Hypotenuse)2


(AM)2 + (BM)2 = (AB)2


(5)2 + (BM)2 = (13)2


(BM)2 = (13)2 – (5)2


(BM)2 = (13 – 5)(13+5)


[ (a2 – b2) = (a + b)(a – b)]


(BM)2 = (8)(18)


(BM)2 = 144


BM = ±12


BM = 12 [taking positive square root]


BC = 2BM or 2MC = 2×12 = 24cm


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