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

1. 1 : 4
2. 3 : 8
3. 2 : 9
4. 1 : 3

Answer 1

Correct Answer - Option 1 : 1 : 4

Calculation:

Let the length and the breadth of the rectangle be L and B respectively.
According to the Question,

Area of Rectangle/Perimeter² = 1/25

⇒ LB/(2(L+B))² = 1/25
⇒ 25LB = 4L² + 4B² + 8LB

⇒ L² + B² = (17/4)LB

Now, Either we solve the Quadratic Equation or Check with the options

There will be two solution, Either B = 1, L = 4 or B = 4 or L = 1
Since B < L,

 ∴ B : L = 1 : 4