Two squares differ in areas by 32 cm². If the difference in their sides is 4 cm, what are the sides of the two squares?

Correct option is A

Given:

Difference in areas of two squares = 32 cm²

Difference in sides of two squares = 4 cm

Formula Used:

Area of a square = side²

Solution:

Let the side of the larger square be x cm.

Then, the side of the smaller square = (x - 4) cm.

The difference in their areas is 32 cm².

x² - (x - 4)² = 32

x² - (x² - 8x + 16) = 32

x² - x² + 8x - 16 = 32

8x - 16 = 32

8x = 32 + 16

8x = 48

x = 48 / 8

x = 6

So, the side of the larger square is 6 cm, and the side of the smaller square is:

x - 4 = 6 - 4 = 2 cm

The sides of the two squares are 6 cm and 2 cm.