The base an height of a triangle are in the ratio $3 : 2$ and its area is $108 c m^{3}$ . Find its base and height.

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Solution

Let the ratio be x
base = 3x height = 2x
area of triangle = 108
$\begin{matrix} \Rightarrow \frac{1}{2} \times 2 x \times 3 x = 108 \Rightarrow 3 x^{2} = 108 \Rightarrow x^{2} = 36 x = 6 B a s e = 3 x = 3 \times 6 = 18 c m h e i g h t = 2 x = 2 \times 6 = 12 c m . \end{matrix}$

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