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

Correct option is B

Given
Ratio of sides = 3:5:7
Perimeter = 300 m

Formula Used
Semi-perimeter (s) = $$\frac{a+b+c}{2}$$​​
Heron's Formula Area = $$\sqrt{s(s-a)(s-b)(s-c)}$$​​

Solution
​$$3x + 5x + 7x = 300 \Rightarrow 15x = 300 \Rightarrow x = 20$$​​
Sides: a=60, b=100, c=140
s = 150
Area = $$\sqrt{150(150-60)(150-100)(150-140)}$$​​
Area = $$\sqrt{150 \times 90 \times 50 \times 10} = \sqrt{6750000} = 1500\sqrt{3} m²$$​​

Final Answer
So the correct answer is (b)