Question

the sides of a triangle are in the ratio 3:5:7 and its perimeter is 300m. find its area

Answer 1

Let coefficient of ratios be X.
then,
3x+5x+7x=300
15x=300
X=20

Sides of triangle are :-
60 m + 100 m + 140 m

By Heron's formula,
We have,
$s = \frac{a + b + c}{2} \\ s = \frac{300}{2} \\ s = 150 \\ area = \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{150(150 - 60)(150 -100)(150 - 140)} \\ = \sqrt{150 \times 90 \times 50 \times 10} \\ = \sqrt{15 \times 9 \times 5 \times 10000} \\ = \sqrt{75 \times {3}^{2} \times {10}^{4} } \\ = \sqrt{75} \times 3 \times {10}^{2} \\ = \sqrt{75} \times 300 \\ = \sqrt{25 \times 3} \times 300 \\ = \sqrt{ {5}^{2} \times 3} \times 300 \\ = 1500 \times \sqrt{3} \\ = 1500 \sqrt{3} {m}^{2}$

Answer 2

Let coefficient of ratios be X.

then,

3x+5x+7x=300

15x=300

X=20

Sides of triangle are :-

60 m + 100 m + 140 m

By Heron's formula,

We have,