Question

The perimeter of a triangle is $300m$. If its sides are in the ratio $3:5:7$. Find the area of the triangle.

• A. $1500\sqrt{5}{m}^2$
• B. $1500m^2$
• C. $1500\sqrt{3}{m}^2$
• D. $1100\sqrt{3}{m}^2$

Answer 1

Answer: (C)

$1500\sqrt{3}{m}^2$

Let, 1 side be = $3x$

2 side be = $5x$

3 side be = $7x$

According to question, $3x+5x+7x=300$

$⟹x=20$

So, sides are $60,100,140$

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

$s=semi-perimeter$

$s=150$, $a=60$, $b=100$, $c=140$

Area=$\sqrt{150(150-60)(150-100)(150-140)}$

$⟹\sqrt{150\left(90\right)\left(50\right)\left(10\right)}$

$⟹1500\sqrt{3}{m}^2$