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Question -

The area of a rectangle remains the same if the length is increased by 7 metres and the breadth is decreased by 3 metres. The area remains unaffected if the length is decreased by 7 metres and breadth is increased by 5 metres. Find the dimensions of the rectangle.



Answer -

Let the length of a rectangle = x m
and breadth = y m
Area = Length x breadth = xy sq. m
According to the condition given,
(x + 7)(y тАУ 3) = xy
=> xy тАУ 3x + 7y тАУ 21 = xy
-3x + 7y = 21 тАж.(i)
and (x тАУ 7) (y + 5) = xy
=>xy + 5x тАУ 7y = xy
5x тАУ 7y = 35 тАж(ii)
(i) from (ii)
2x = 56
=> x = 28
Substituting the value of x in (i)
-3 x 28 + 7y = 21
тАУ 84 +7y = 21
=> 7y = 21 + 84 = 105
y = 15
Length of the rectangle = 28 m and breadth = 15 m

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