Question

The sides of a triangular field are in the ratio $5:3:4$ and its perimeter is $180m$. Find its area.

Answer 1

Let the sides of the triangular field be $5a,3a,4a$.
Perimeter of the triangle $=$ Sum of all sides $=5a+3a+4a=12a$
Given, perimeter of the triangular fied $=180m$
$\Rightarrow 12a=180m$
$a=15m$
So, the sides of the triangular field are $5a=75m,3a=45m,4a=60m$.

Area of triangle with sides $a,b,c$:
$s=\frac{a+b+c}{2}$

And $A=\sqrt{s(s-a)(s-b)(s-c)}$.
For the triangular field with sides $75m,45m$ and $60m$, $s=\frac{75+45+60}{2}=90m$
Area of the triangular field with sides $75m,45m$ and $60m$ $=\sqrt{90(90-75)(90-45)(90-60)}=\sqrt{90\times 15\times 45\times 30}=\sqrt{15\times 6\times 15\times 15\times 3\times 15\times 2}=15\times 15\times 6=1350m^2$