Question

The perimeter of $△$ is 150m and its sides are in the ratio 5:12:13.Find the area of $△$ .

Answer 1

So let the sides be 5x, 12x, 13x
5x + 12x + 13x = 150
30x = 150
x = 5
side lengths are 25, 60, 65 m
and semiperimeter $s=\frac{a+b+c}{2}=75$
So by using Heron's formula
area of the triangle $=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{75(75-25)(75-60)(75-65)}$
$=\sqrt{\mathrm{75.50.15.10}}$
$=\sqrt{25\times 3\times 2\times 25\times 5\times 3\times 5\times 2}$
$=\sqrt{(25{)}^2\times 3^2\times 2^2\times 5^2}$
$=25\times 3\times 2\times 5$
$=750sqm$