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

Given:

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

To do:

We have to find the area of the triangle.

Solution:

Let the sides of the triangle be $3x, 5x$ and $7x$.

This implies,

$3x+5x+7x=300\ m$

$15x=300\ m$

$x=\frac{300}{15}$

$x=20\ m$

Therefore,

$a=3x=3(20)=60\ m$

$b=5x=5(20)=100\ m$

$c=7x=7(20)=140\ m$

$s=\frac{\text { Perimeter }}{2}$

$=\frac{300}{2}$

$=150$

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

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

$=\sqrt{150 \times 90 \times 50 \times 10}$

$=\sqrt{3 \times 5 \times 10 \times 3 \times 3 \times 10 \times 5 \times 10 \times 10}$

$=10 \times 10 \times 5 \times 3 \times \sqrt{3} \mathrm{~m}^{2}$

$=1500 \sqrt{3} \mathrm{~m}^{2}$

The area of the triangle is $1500\sqrt{3}\ m^2$. 

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Updated on: 10-Oct-2022

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