Question

Find area of the triangle if the sides of the triangle are in the ratio 12:17:25 and the perimeter is 270 m.

• A. 2250

Answer 1

The correct option is A 2250
The area (A) of a triangle can be calculated using Heron's formula, given by:
$A=\sqrt{s(s-a)(s-b)(s-c)}$,
where a, b and c are its sides and s is its semi-perimeter.
[i.e., $s=\frac{a+b+c}{2}$]

Given, the sides are in the ratio 12:17:25 and the perimeter is 270 m.
Let the common factor be ‘x’
Then, $12x+17x+25x=270$
$\Rightarrow 54x=270$
$\Rightarrow x=5$
$\therefore \text{The lengths of the sides are 60 m, 85 m and 125 m.}$
Then,
$s=\frac{(60+85+125)}{2}$ = 135 m
$\therefore A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{135(135-60)(135-85)(135-125)}=\sqrt{135\times 75\times 50\times 10}=\sqrt{5\times 9\times 3\times 25\times 3\times 25\times 2\times 5\times 2}=5\times 9\times 25\times 2=2250{\text{m}}^2$