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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