Question

In an isosceles triangle one side is $12cm$ (other than the equal sides) and its perimeter is $26cm$. Find the area of the triangle.

• A. √450
• B. √468
• C. √78
• D. √420

Answer 1

The correct option is B

√468

Let each of its equal sides be $x.$
Then, $2x+12=26$ $\Rightarrow x=7cm$
Hence, the sides are $\text{7 cm, 7 cm and 12 cm}$.
Using the Heron's formula,
Area (A) $=\sqrt{s(s-a)(s-b)(s-c)}$
$\text{Semi-perimeter, s}=\frac{\text{perimeter}}{2}$
$s=\frac{26}{2}$ $=13cm$
$A=\sqrt{13(13-7)(13-7)(13-12)}$
$=\sqrt{13\times 6\times 6\times 1}$
$=\sqrt{468}c{m}^2$