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 :

A. 21 cm²

B. $$0.5\sqrt {21} $$ cm²

C. $$1.5\sqrt {21} $$ cm²

D. $$2\sqrt {21} $$ cm²

Answer: Option D

Solution(By Examveda Team)

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
$$\eqalign{ & s = \frac{{{\text{a + b + c}}}}{2} \cr & \,\,\,\,\,\,\,\, = \left( {\frac{{14}}{2}} \right)cm \cr & \,\,\,\,\,\,\,\, = 7cm \cr} $$
(s - a) = 2 cm, (s - b) = 2 cm, (s - c) = 3 cm
∴ Area of the triangle :
$$\eqalign{ & = \sqrt {7 \times 2 \times 2 \times 3} \cr & = 2\sqrt {21} \,c{m^2} \cr} $$