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Question
The base of an isosceles triangle is 24 cm and its area is 192 sq. cm. Find its perimeter.
Solution
It is given that
Area = 192 sq.cm
base = 24 cm
Knowing the length of the equal side, a and base, b of an isosceles triangle, the area can be calculated using the formula,
A = `1/4 xx b xx sqrt (4a^2 - b^2`
Let 'a' be the length of an equal side.
Area = `1/4 xx b xx sqrt(4a^2 - b^2)`
192 = `1/4 xx 24 xx sqrt(4a^2 - 576)`
192 = `6 sqrt(4a^2 - 576)`
`sqrt(4a^2 - 576` = 32
4a2 - 576 = (32)2
4a2 - 576 = 1024
4a2 = 1024 + 576
4a2 = 1600
a = 20 cm
Hence, perimeter = 20 + 20 + 24
= 64 cm
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