The perimeter of an isosceles triangle is equal to 14 cm and the lateral side is to the base in the ratio 5 : 4. The area of the triangle is :

Answer: Option D

Let the sides of the triangle be 5x, 5x and 4x cm respectively
Then,
5x + 5x = 4x + 14
⇒ 14 x = 14
⇒ x = 1
So, a = 5 cm, b = 5 cm, c = 4 cm
$$\begin{array}{rl}& s=\frac{\text{a + b + c}}{2}\\ & =\left(\frac{14}{2}\right)cm\\ & =7cm\end{array}$$
(s - a) = 2 cm, (s - b) = 2 cm, (s - c) = 3 cm
∴ Area of the triangle :
$$\begin{array}{rl}& =\sqrt{7\times 2\times 2\times 3}\\ & =2\sqrt{21}c{m}^2\end{array}$$