The area of a rectangle is 9/20 times the area of a square. If the length and breadth of the rectangle are in the ratio 5 : 4, then find the ratio of perimeters of rectangle and square.

area of rectangle = $$ \frac{9}{20} \times $$ area of square

ratio of length and breadth = 5 : 4

according to question

$$ 5x \times 4x = \frac{9}{20} \times a^{2} $$

$$ 20x^{2} = \frac{9}{20} \times a^{2} $$

$$ \frac{x^{2}}{a^{2}} = \frac{9}{400} $$

$$ \frac{x}{a} = \frac{3}{20} $$

length = $$ 5 \times 3 = 15 $$

breadth = $$ 4 \times 3 = 12 $$

perimeter of rectangle = $$ 2(l + b) =2(15 + 12) = 54 $$

perimeter of square = $$ 4a = 4 \times 20 = 80 $$

ratio of perimeters of rectangle and square = $$ \frac{54}{80} = \frac{27}{40} $$