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

• A. 1:4
• B. 2:9
• C. 1:3
• D. 3:8

Answer 1

The Correct Option is A

The correct answer is (A):
Let the length and the breadth of the rectangle be L and B respectively.
Given that Area of triangle/Perimeter2 = 1/25 ⇒ L×B/(2(L+B))2 = 1/25
⇒ 25LB = 4L2+4B2+8LB
= L2+B2 = (17/4)LB
(Note: Alternatively, we can also solve the quadratic equation in terms of L/B and we’d get the same result, i.e. 4 or ¼ )
Since B < L, the ratio B : L = 1 : 4