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.
A
24cm
B
36cm
C
72cm
D
144cm
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Area = \(\frac{1}{2} \times base \times height\)
\(height : base = 1 : 3\)
\(\implies base = 3 \times height\)
Let height = h;
Area = \(\frac{1}{2} \times 3h \times h = 216\)
\(3h^2 = 216 \times 2 = 432\)
\(h^2 = \frac{432}{3} = 144\)
\(h = \sqrt{144} = 12.0 cm\)
\(\therefore base = 3 \times 12 = 36 cm\)
Source: Myschool Past Questions Archive (Record #26409)