The area of the square formed on the diagonal of a rectangle as its side is 108 1 3 more than the ar...........

Quantitative Aptitude ( CCS) Mensuration 2D

The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?

1 m

2 m

3 m

4 m

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Explanation:

Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b²) = (1 + 108 1/3 %)lb
=> l²+ b² = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l² + b²)/lb = 25/12
12(l²+ b²) = 25lb
Adding 24lb on both sides
12l²+ 12b² + 24lb = 49lb
12(l² + b² + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)² = 49lb
=> 12(14)² = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.