The perimeter of one square is 52 metre and that of another is 20 metre. What is the perimeter of the square whose area is equal to the difference of the areas of the two squares?

Correct option is A

Given:

The perimeter of the first square is 52 meters.

The perimeter of the second square is 20 meters.

Formula Used:

Perimeter of a square is given by the formula:

​$$P = 4 \times \text{side}$$​​​​

Area of a square is given by:

Area = $$\text{side}^2$$

Solution:

For the first square:

side₁​ = $$\frac{52}{4} = 13 \, \text{m}$$​​

So, the area of the first square is:

Area₁​ = $$13^2 = 169 \, \text{m}^2$$​​

For the second square:

side₂​ = $$\frac{20}{4} = 5 \, \text{m}$$​​

So, the area of the second square is:

Area₂​ = $$5^2 = 25 \, \text{m}^2$$​​

The difference in areas is:

​$$\text{Area}_1 - \text{Area}_2 = 169 - 25 = 144 \, \text{m}^2$$​​

Let the side of the new square whose area is $$144 \, \text{m}^2$$​ be side₃​.

So, the side of the new square is:

​$$\text{side}_3^2 = 144 \quad \Rightarrow \quad \text{side}_3 = \sqrt{144} = 12 \, \text{m}$$​​

Finally, the perimeter of the new square is:

​$$P_3 = 4 \times \text{side}_3 = 4 \times 12 = 48 \, \text{m}$$​​

The perimeter of the new square is 48 meters.

Thus, the correct option is (a) 48 m