Question

Choose the correct answer of the following question:


The base and height of a triangle are in the ratio 3:4 and its area is 216 cm². The height of the triangle is

(a) 18 cm (b) 24 cm (c) 21 cm (d) 28 cm

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{base}\mathrm{of}\mathrm{the}\mathrm{triangle}\mathrm{be}3x\mathrm{and}\mathrm{its}\mathrm{height}\mathrm{be}4x. \\ \mathrm{As},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{triangle}=216{\mathrm{cm}}^2 \\ \Rightarrow \frac{1}{2}\times \mathrm{Base}\times \mathrm{Height}=216 \\ \Rightarrow \frac{1}{2}\times 3x\times 4x=216 \\ \Rightarrow 6x^2=216 \\ \Rightarrow x^2=\frac{216}{6} \\ \Rightarrow x^2=36 \\ \Rightarrow x=\sqrt{36} \\ \Rightarrow x=6\mathrm{cm} \\ \mathrm{So},\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{triangle}=4\times 6=24\mathrm{cm} \end{gathered}$$

Hence, the correct answer is option (b).