Question

The ratio of area of a square to the perimeter of this square of side $\frac{3}{2}$ unit is__

• A. $\frac{9}{24}$
• B. $\frac{2}{4}9$
• C. $\frac{27}{2}$
• D. $\frac{9}{4}$

Answer 1

The correct option is A $\frac{9}{24}$

Given, side of square $=\frac{3}{2}$ unit.
As we know,
Area of a square $={\text{side}}^2=x^2$
$={\left(\frac{3}{2}\right)}^2=\frac{3\times 3}{2\times 2}=\frac{9}{4}{\text{unit}}^2$

Perimeter of a square $=4x=4\times \frac{3}{2}=2\times 3=6unit$

A ratio of the area of a square to the perimeter of a square = Area of a square $÷$ Perimeter of a square
$=\frac{9}{4}÷6=\frac{9}{4}\times \frac{1}{6}=\frac{9}{(4\times 6)}$

Hence, $\frac{\text{Area of a square}}{\text{Perimeter of square}}=\frac{9}{4\times 6}=\frac{9}{24}$

Option (a) is correct.