Question

The perimeter of a triangular field is 144 m and the ratio of the sides is 3 : 4 : 5. Find the area of the field.

Answer 1

Perimeter of the field = 144 m
Ratio in the sides = 3 : 4 : 5
Sum of ratios -3 + 4 + 5 = 12

$\therefore$ First side = $\frac{144}{12}\times 3=36m$

Second side = $\frac{144}{12}\times 4=48m$

and third side = $\frac{144}{12}\times 5=60m$

Now, $s=\frac{Perimeter}{2}=\frac{144}{2}=72m$

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

= $\sqrt{72(72-36)(72-48)(72-60)}$

= $\sqrt{72\times 36\times 24\times 12}$

=$\sqrt{12\times 2\times 3\times 12\times 3\times 12\times 2\times 12}$

= $12\times 12\times 3\times 2=864m^2$