The sides of a triangular plot are in the ratio 3 : 5 : 7; its perimeter is 300m. Find its area.

Given ratio is 3 : 5: 7
Total parts : 3+5+7 = 15
Perimeter = 300 m
One part : \(\frac{300}{15} \,=\,20\,m\)
Therefore,
First side : \(3 × 20\,= \,60\,m\)
Second side : \(5 × 20\,=\,100\,m\)
Third side : \(7 × 20\,=\,140\,m\)

\(s = \frac{300}{2}\,=\,150\,m\)

\(\begin{aligned}Area &= \sqrt{150(150−60)(150−100)(150−140)} \\ &= \sqrt{150 × 90 × 50 × 10} \\ &= \sqrt{6750000} \\ &= \sqrt{675 × 10000} \\ &= 100 \sqrt{675} \\ &= 100 \sqrt{15^2 × 3} \\ &= 100 × 15 \sqrt{3} \\ &= 1500 \sqrt{3}\end{aligned}\)
Using √3 ≈ 1.732,
\(Area ≈ 1500 × 1.732\,=\,2598\,m^2\)
The area is 1500√3 or 2598 m\(^2\).