Question 58

Perimeter of an isosceles triangle is 32 cm. The base is $$\frac{6}{5}$$times the equal side. What is the area?

Solution

let one side be x

then the equal sides be 2x

base is 6/5 times of x = $$ \frac{6}{5}x $$

perimeter = 32 ( given )

perimeter = 2x + $$ \frac{6}{5}x $$

32 = 2x + $$ \frac{6}{5}x $$

solving x = 10

now sides are 10, 10, 12( $$ \frac{6}{5} \times 10 $$ )

area = $$ \frac{1}{4} b \sqrt{P(P - 2b)} $$

= $$ \frac{1}{4} 12 \sqrt{32(32 - 2 \times 12)} $$

= $$ 48 cm^2 $$

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