Question

In a parallelogram, the base and corresponding height are in the ratio 3:2. If the area of the parallelogram is $216c{m}^2$, then find the measures its base and height.

• A. 13 cm, 12 cm
• B. 18 cm, 12 cm
• C. 19 cm, 14 cm
• D. 24 cm, 16 cm

Answer 1

The correct option is B 18 cm, 12 cm

Let the base and the corresponding height of the parallelogram be $3x$ and $2x$ respectively.

Area of a parallelogram = base $\times$ height
$=3x\times 2x$
$=6x^2$

Now, it is given that area of the parallelogram is 216 cm${}^2$.
$\Rightarrow 216=6x^2$
$\Rightarrow x^2=36$
$\Rightarrow x=\pm 6$

Since length cannot be negative, we have $x=6$
Thus, base and corresponding height of the parallelogram are 18 cm and 12 cm long respectively.