Question

The base of an isosceles triangle is $12cm$ and its perimeter is $32cm$. What is its area?

• A. $12$ $c{m}^2$
• B. $36c{m}^2$
• C. $24c{m}^2$
• D. $48c{m}^2$

Answer 1

Answer: (D)

$48c{m}^2$

Let $△ABC$ be an isoceles $△$, such that $AB=BC$ perimeter $=a+12+a=2a+12$

Also, $2a+12=32cm\Rightarrow a=\frac{32-12}{2}=10cm$

$\therefore ar△ABC=\sqrt{s(s-a)(s-b)(s-c)},s=\frac{a+b+c}{2}=\frac{32}{2}=16cm$

$=\sqrt{16(16-10)(16-10)(16-12)}=\sqrt{16\times 6\times 6\times 4}=4\times 6\times 2$

$=48{cm}^2$