Question

The sides of a triangle are in the ratio 2 : 3 : 4. If the semi-perimeter of the triangle is 36 cm, then what is its area?

• A.
  $48c{m}^2$
• B.
  $\sqrt{17}c{m}^2$
• C.
  $48\sqrt{15}c{m}^2$
• D.
  $97c{m}^2$

Answer 1

The correct option is C

$48\sqrt{15}c{m}^2$
Given that the sides of the triangle are in ratio 2 : 3 : 4.

Let the sides of the triangle be 2x, 3x and 4x, where x is any natural number.

It is given that the semi-perimeter, (s) of the triangle is 36 cm.

$\Rightarrow \frac{3x+3x+4x}{2}=36cm\Rightarrow 9x=72cm\Rightarrow x=8cm$

Therefore, the sides of the triangle are

$8\times 2=16cm,8\times 3=24cmand8\times 4=32cm.$

Let a = 16 cm, b = 24 cm and c = 32 cm.

$\therefore \text{Area of the triangle}=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{36(36-16)(36-24)(36-32)}=\sqrt{36\times 20\times 12\times 4}=6\times 4\times 2\sqrt{3\times 5}=48\sqrt{15}c{m}^2$
Thus, the area of the triangle is $48\sqrt{15}c{m}^2$.

Hence, the correct answer is option (c).