Q72 of 82 Page 4

The area of an isosceles triangle is 60 cm2 and the length of each of its equal sides is13 cm. Find its base. (CBSE 2015)


Let ABC be the given isosceles triangle in which AB=AC = 13 cm


Let BC = 2x cm.


Then BD = DC = x cm


In ΔABC,


AB2 = AD2 + BD2


132 = AD2 + x2




Now area = 60 cm2


⇒ 1/2 (BC × AD) = 60



⇒ x2(169 – x2) = 3600


⇒ x4 – 169 x2 + 3600 = 0


⇒ (x2 – 144)(x2 – 25) = 0


⇒ x2 = 144 or x2 = 25


⇒ x = 12 or x = 5


Hence base = 2x


= 24 or 10

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