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Question
The area of the isosceles triangle is 60 cm2, and the length of each one of its equal side is 13cm. Find its base.
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Solution
Area of a isosceles triangle = `("b" xx sqrt (4"a"^2 - "b"^2))/4`
Here, area = 60, a = 13. Putting this in equation and squaring both sides, we get
(60 x 4)2 = b2 (4 x 13 x 13 - b2 )
⇒ 57600= b2 x (676 - b2) = 676 b2 - b4
⇒ b4 - 676b2 +57600 = 0
⇒ b4 -100b2 - 576b2 + 57600 = 0
⇒ b2 (b2 - 100) - 576 (b2 - 100) = 0
⇒ (b2 - 100 )(b2 - 576) = 0
⇒ b2 = 576 , b2 = 100
⇒ b = 24 , b = 10
⇒ Hence base can be either 24 or 10 cm.
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