The area of a rectangle and the square of its perimeter are in the ratio 1 ∶ 25. Then the lengths of the short

Question

The area of a rectangle and the square of its perimeter are in the ratio 1 ∶ 25. Then the lengths of the shorter and longer sides of the rectangle are in the ratio

Accepted Answer

1:4. Let 'a' and 'b' be the length of sides of the rectangle. (a > b) Area of the rectangle = a*b Perimeter of the rectangle = 2*(a+b) ⇒ \Rightarrow ⇒ a ∗ b ( 2 ∗ ( a + b ) ) 2 = 1 25 \dfrac{a*b}{(2*(a+b))^2}=\dfrac{1}{25} ( 2 ∗ ( a + b ) ) 2 a ∗ b ​ = 25 1 ​ ⇒ \Rightarrow ⇒ 25 a b = 4 ( a + b ) 2 25a