The base and height of a triangle are in the ratio 3:4 and the area of the triangle is 96cm². Find the base and height of the triangle.

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Since the base and height of a triangle are in the ratio 3:4.
So suppose the base and height of triangle are 3x and 4x respectively.
So, area of triangle = $\frac{1}{2}\times \mathrm{base}\times \mathrm{height} = \frac{1}{2}\times 3x\times 4x = 96 {\mathrm{cm}}^2$
$$\begin{gathered} \Rightarrow 6x^2 = 96 \\ \Rightarrow x^2 =1 6 \\ \Rightarrow x = \sqrt{16} = 4 \end{gathered}$$
So base of triangle = $3\times 4$ = 12 cm
And height of triangle = $4\times 4$ = 16 cm