Question

In an isosceles triangle, the unequal side is 12cm and its perimeter is 26cm. Find the area of the triangle.

• A. $5\sqrt{13}c{m}^2$
• B. $6\sqrt{13}c{m}^2$
• C. $6\sqrt{10}c{m}^2$
• D. $24c{m}^2$

Answer 1

The correct option is B

$6\sqrt{13}c{m}^2$

Perimeter = 26

Equal sides $=\frac{(26-12)}{2}=7cm$ each

$S=\frac{26}{2}=13$

Now by hero’s formula

Area $=\sqrt{s(s-a)(s-b)(s-c)}$

Area $=\sqrt{13(13-12)(13-7)(13-7)}$

= $=\sqrt{13\times 6\times 6}$

= $6\sqrt{13}c{m}^2$