Question 90

The perimeter of an isosceles triangle is 32 cm and each of the equal sides is 5/6 times of the base. What is the area $$(in cm^{2})$$ of the triangle ?

Solution

Given $$S = \frac{5}{6}\times x$$

perimeter = 32

s + s + x = 32

2s + x = 32

2(5/6)x + x = 32

x = 12, s = 10.

let h be the height of the triangle,

$$h=\sqrt{s^{2}-(a/2)^{2}}$$ = $$8$$

area of triangle = $$\frac{1}{2}\times bh$$ = $$\frac{1}{2}\times 12\times 8= 48$$

so the answer is option B.

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