Question

The areas of two squares are in the ratio $25:36$. What is the ratio of their perimeters? Express your answer in the form $\mathrm{a}:\mathrm{b}$.

Answer 1

Step-1: Find the ratio of sides:

Let, the sides of the square $A$ and square $B$ are $\mathrm{a},\mathrm{b}$ respectively.

The area of square $A$$=a^2.$

And

The area of square $B$$=b^2.$

Now, it is given,

$\begin{array}{rcl}\frac{a^2}{b^2}& =& \frac{25}{36}\\ & \Rightarrow & \frac{a}{b}=\sqrt{\frac{25}{36}}\\ & =& \frac{5}{6}...\left(1\right)\end{array}$

Step-2: Find the ratio of the perimeter:

The perimeter of square $A$ and square $B$ are $4a,4b$ respectively.

Now,

Ratio of perimeter $=\frac{4a}{4b}$

$=\frac{a}{b}$

$a:b=5:6\mathbf{[}\mathbf{from}\mathbf{}\mathbf{1}\mathbf{]}$

Hence, the ratio of the perimeter is $5:6$.