Question

Mark (✓) against the correct answer:
The base of a triangle is four times its height and its area is 50 m². The length of its base is
(a) 10 m
(b) 15 m
(c) 20 m
(d) 25 m

Answer 1

(c) 20 m

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{triangle}\mathrm{be}\mathit{}x\mathrm{m}\mathrm{and}\mathrm{its}\mathrm{base}\mathrm{be}4x\mathit{}\mathrm{m}\mathrm{respectively}. \\ \mathrm{Then},\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{triangle}=\left(\frac{1}{2}\times 4x\times x\right)m^2 \end{gathered}$$
$=2x^2{\mathrm{m}}^2$
$$\begin{gathered} \mathrm{But},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{triangle}is50{\mathrm{m}}^2. \\ \therefore 2x^2=50 \\ \Rightarrow x^2=\frac{50}{2} \\ \Rightarrow x^2=25 \\ \Rightarrow x=\sqrt{25} \\ \Rightarrow x=5 \\ \therefore L\mathrm{ength}\mathrm{of}\mathrm{its}\mathrm{base}=\left(4\times 5\right)\mathrm{m}=20m \end{gathered}$$