The length of a rectangle is 30 cm and its width is $$\frac{2}{3}$$​ of its length. What will be the area of a square having a perimeter that is identical to the perimeter of the rectangle described here?

Correct option is C

Given:
Length of the rectangle ( L) = 30 cm.
Width of the rectangle ( W ) = $$\frac{2}{3}$$​  of its length.
Formula Used:
Perimeter of a rectangle = 2(L + W) 
Perimeter of a square =$$4 \times \text{side}$$​

Area of a square $$= \text{side}^2$$​
Solution:
$$W = \frac{2}{3} \times L = \frac{2}{3} \times 30 = 20 \, \text{cm}$$​​
$$\text{Perimeter of rectangle} = 2(L + W) = 2(30 + 20) = 2 \times 50 = 100 \, \text{cm}$$​

Let the side of the square be s. Since the perimeter of the square is equal to the perimeter of the rectangle:

4s = 100
$$s = \frac{100}{4} = 25 \, \text{cm}$$​

​$$\text{Area of square} = s^2 = 25^2 = 625 \, \text{cm}^2$$​​