Question

The area of a parallelogram is $27{\text{unit}}^2$. If height of the parallelogram is one-third of length of the base, find the length of base of the parallelogram?

• A. 3 units
• B. 9 units
• C. 6 units
• D. 12 units

Answer 1

The correct option is B 9 units

Let's draw a parallelogram ABCD.
Lets assume length of base to be $x\text{units}$

Given: Height of the parallelogram is one-third of length of the base

Hence, Height of parallelogram $=\frac{x}{3}\text{units}$

Area of parallelogram $=27{\text{unit}}^2$

As we know,
Area of parallelogram = Base $\times$ Height
$27=x\times \frac{x}{3}$

$x^2=27\times 3=81$

$x=\sqrt{81}=\sqrt{9\times 9}=9\text{units}$

Hence, Length of base of the parallelogram = 9 units
Option (b) is correct.