Question

The area of a triangle is 1176 cm^2. If the base and height of the triangle are in the ratio 3 : 4, then the height of the triangle is
(a) 42 cm
(b) 52 cm
(c) 54 cm
(d) 56 cm

Answer 1

(d) 56 cm

Let the base and height of the triangle be $3x$ cm and $4x$ cm, respectively.

Now,

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{triangle}=\frac{1}{2}\times \mathrm{base}\times \mathrm{height} \\ \Rightarrow 1176=\frac{1}{2}\times 3x\times 4x \\ \Rightarrow 1176=6x^2 \end{gathered}$$

$\Rightarrow x=\sqrt{\frac{1176}{6}}=\sqrt{196}=14$

∴ Height of the triangle$=4x=4\times 14=56\mathrm{cm}$