Question

The base and height of the triangle are in the ratio 3:2. If the area of the triangle is 243 cm${}^2$, find the base and height of the triangle.

• A. Base = 18 cm, Height = 27 cm
• B. Base = 12 cm, Height = 18 cm
• C. Base = 27 cm, Height = 54 cm
• D. Base = 27 cm, Height = 18 cm

Answer 1

The correct option is D

Base = 27 cm, Height = 18 cm

Let the common ratio be x
Then height of triangle = 2x
The base of triangle = 3x
Area of triangle = 243 cm${}^2$
Area of triangle = $\frac{1}{2}$ $\times$ b $\times$ h

243 = $\frac{1}{2}$ $\times$ 3x $\times$ 2x
$\Rightarrow$ 3x${}^2$ = 243
$\Rightarrow$ x${}^2$ = 243/3
$\Rightarrow$ x = $\sqrt{81}$
$\Rightarrow$ x = $\sqrt{9\times 9}$
$\Rightarrow$ x = 9
Therefore, height of triangle = 2 $\times$ 9
= 18 cm
Base of triangle = 3x
= 3 $\times$ 9
= 27 cm