In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length

• Mensuration

In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side?

1. 2 : 5
2. √3 : 2
3. 3 : 4
4. 1 : √3

Answer

Let L and B be the length and breadth of the rectangle.

Sum of adjacent sides = L + B

Length of diagonal = √(L²+B²)

According to the question,

(L + B) - √(L²+B²) = L/2

L/2 + B = √(L²+B²)

L + 2B = 2√(L²+B²)

L² + 4B² + 4LB = 4L² + 4B²

4B = 3L or B/L = 3/4

The correct option is C.