Question

If an isosceles triangle has perimeter 18 cm and base 8 cm, then its area is ${cm}^2$.

• A. $45c{m}^2$
• B. $24c{m}^2$
• C. $36c{m}^2$
• D. $12c{m}^2$

Answer 1

The correct option is D $12c{m}^2$

Given: Perimeter of an isosceles triangle is 18 cm.
Let each of the equal sides of the isosceles triangle be $x$.
Then, $2x+8=18$ $\Rightarrow x=5cm$
Hence, the sides are $\text{5 cm, 5 cm and 8 cm}$.
Using the Heron's formula,
$Area\left(A\right)=\sqrt{s(s-a)(s-b)(s-c)}$
where s = semi-perimeter and a, b, c are the three sides of the triangle.
$\text{Semi-Perimeter (s)}=\frac{\text{Perimeter}}{2}$
$=\frac{18}{2}$
$=9cm$
$A=\sqrt{9(9-5)(9-5)(9-8)}$
$=\sqrt{9\times 4\times 4\times 1}$
$=\sqrt{144}c{m}^2$
$=12c{m}^2$