Question

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

• A. $48$ sq cm
• B. $36$ sq cm
• C. $24$ sq cm
• D. $12$ sq cm

Answer 1

The correct option is A $48$ sq cm

Let the congruent sides of the isosceles triangle $=a$ and the base $=b$.

Given, $b=12cm$

Perimeter of the triangle $=$Sum of all sides $=$ a + a + b $=32$

$\Rightarrow 2a+12=32$

On solving, a $=10cm$

Since the height of the triangle, divides it into two right angled triangles,

$a^2=h^2+{\left(\frac{b}{2}\right)}^2\Rightarrow {10}^2=h^2+6^2$

$h^2=100-36=64$

$h=\sqrt{64}=8$ cm

Area of triangle $=\frac{1}{2}\times base\times height=\frac{1}{2}\times 12\times 8=48$ sq cm