Question

The ratio of area of a parallelogram to perimeter of the parallelogram is $1:2$. Length of base of this parallelogram is 4 units and length of adjacent side to the base is 3 units. Find the height of the parallelogram.

• A. $\frac{3}{4}$ unit
• B. $\frac{5}{7}$ unit
• C. $\frac{4}{7}$ unit
• D. $\frac{7}{4}$ units

Answer 1

The correct option is D $\frac{7}{4}$ units

Let's draw a parallelogram ABCD of base 4 units.
Lets assume height to be $h$
Given,
Base of parallelogram $=4$ units

As we know,
Area of the parallelogram = Base $\times$ Height
$=4\times h$

Given,
AC = BD = 3 units
AB = CD = 4 units

Perimeter of parallelogram = AB + BD + DC + CA
$=4+3+4+3=14$ units

Given,
$\frac{\text{Area of parallelogram}}{\text{Perimeter of parallelogram}}=\frac{1}{2}$

$\frac{4\times h}{14}=\frac{1}{2}$

$h=\frac{1\times 14}{2\times 4}=\frac{7}{4}$ units

Option (d) is correct.