The perimeter of an isosceles triangle is 32cm.The ratio of equal side to its base is 5:4.Find the area?

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Solution

The perimeter of isosceles triangle = 32cm

perimeter of isosceles triangle =( 2 × equal side )+ base
let length of equal side be 5x and base be 4x
then

2 × 5x + 4x = 32 cm
10x + 4x = 32cm
14x = 32 cm
x= 2.285 cm
length of equal side = 5×2.285= 11.425cm
length of base = 4×2.285=9.14cm
area of isosceles triangle=b×(1/4)×√(4a^2-b^2)
= 9.14×(1/4)√(4×130.53-83.53)
=2.285√438.59
=2.285×20.94
=47.847 cm^2

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