The base and height of a triangle are in the ratio $4:3$. If its area is $96 ext{ cm}^{2}$, find its base.

Question

The base and height of a triangle are in the ratio $4:3$. If its area is $96 	ext{ cm}^{2}$, find its base.

Aicharya · Accepted Answer

Let $b = 4k$, $h = 3k$. Area $= \dfrac{1}{2}\cdot 4k \cdot 3k = 6k^{2} = 96 \Rightarrow k^{2} = 16 \Rightarrow k = 4$. Base $= 4k = 16$ cm.

The base and height of a triangle are in the ratio $4:3$. If its area is $96 \text{ cm}^{2}$, find its base.