The height and base of a triangle are in ratio 1:3 respectively. If the area…

The height and base of a triangle are in ratio 1:3 respectively. If the area of the triangle is 216 cm(^2), find the length of the base.

Correct Answer: Option B

Explanation

Area = (frac{1}{2} times base times height)

(height : base = 1 : 3)

(implies base = 3 times height)

Let height = h;

Area = (frac{1}{2} times 3h times h = 216)

(3h^2 = 216 times 2 = 432)

(h^2 = frac{432}{3} = 144)

(h = sqrt{144} = 12.0 cm)

(therefore base = 3 times 12 = 36 cm)