The perimeter of a rectangle is 42 m If the area of the square formed on the diagonal of the rectang...........

Quantitative Aptitude ( CCS) Mensuration 2D

The perimeter of a rectangle is 42 m. If the area of the square formed on the diagonal of the rectangle as its side is 1 1/12 % more than the area of the rectangle, find the longer side of the rectangle.

11 m

16 m

12 m

none of these

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Explanation:

Let the sides of the rectangle be l and b
respectively.
From the given data,
√(l² + b²) = (1 + 1 1/12) lb
=> l² + b²= (1 + 13/12) lb = 25/12 * lb
12(l²+ b²) = 25 lb
Adding 24 lb on both sides
12l²+ 12b²+ 24lb = 25 lb12(l2+ b²+ 2lb) = 49 lb12(l + b)²= 49lb
but 2(l + b) = 42 => l + b = 21
So 12(21)²= 49lb
Solve, we get lb = 108
Since l + b = 21, longer side = 12 m