Question

The perimeter of a triangular park is $180m$ and its sides are in the ratio $5:6:7$. Find the area of the park.

• A. $600\sqrt{6}$ $m^2$
• B. $300\sqrt{6}$ $m^2$
• C. $900\sqrt{6}$ $m^2$
• D. $1800\sqrt{6}$ $m^2$

Answer 1

Answer: (A)

$600\sqrt{6}$ $m^2$

Let the sides of the triangle be $5a,6a,7a$.
Perimeter of the triangle $=$ Sum of all sides $=5a+6a+7a=18a$
Given, perimeter of the triangle $=180m$
$=>18a=180m$
$a=10m$
So, the sides of the triangle are $5a=50m,6a=60m,7a=70m$.

For triangle with sides 50 m, 60 m and 70 m, $s=\frac{50+60+70}{2}=90m$

Area of the triangle $=\sqrt{90(90-50)(90-60)(90-70)}$

$=\sqrt{90\times 40\times 30\times 20}$

$=\sqrt{30\times 3\times 20\times 2\times 30\times 20}$

$=30\times 20\times \sqrt{6}$

$=600\sqrt{6}{m}^2$