The sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 300m. Find its area.

Correct option is C

Given:

Ratio of sides = 5 : 12 : 13

Perimeter = 300 m​​

Formula Used:

​$$\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}$$​​

Solution: 

A triangle with sides in the ratio 5 : 12 : 13 is a right-angled triangle (Pythagorean triple)

Sum of ratio = 30

​$$\frac{300}{30} = 10$$ (Means 1 unit = 10)

So, sides are: 50 m, 120 m, and 130 m

Since $$50^2 + 120^2 = 130^2$$​, triangle is right-angled.

Base = 50 m, Height = 120 m

​$$\text{Area} = \frac{1}{2} \times 50 \times 120 = 25 \times 120 = 3000 \text{ m}^2$$​​

Thus, the correct option is (c) 3000 m²