The breadth of a rectangle is 4/5 of the radius of a circle. The radius of the circle is 1/5 of the side of a square, whose area is 625 $$cm^{2}$$. What is the area of the rectangle if the length of rectangle is 20 cm?

Let's assume the length and breadth of a rectangle are 'L' and 'B' respectively.

Let's assume the radius of circle and side of a sqaure are 'r' and 'a' respectively.

The breadth of a rectangle is 4/5 of the radius of a circle.

$$B=\frac{4}{5}r$$    Eq.(i)

The radius of the circle is 1/5 of the side of a square.

$$r=\frac{1}{5}a$$ Eq.(ii)

area of square is 625 $$cm^{2}$$.

$$a^2\ =\ 625$$

$$a^2\ = 25^2$$

a = 25 cm

Put the value of 'a' in Eq.(ii).
$$r=\frac{1}{5}\times25$$

r = 5 cm 

Now put the value of 'r' in Eq.(i).

$$B=\frac{4}{5}\times5$$

B = 4 cm

Area of the rectangle if the length of rectangle is 20 cm.

Area of the rectangle = $$L\times\ B$$

= $$20\times\ 4$$

= 80 $$cm^{2}$$