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 1

Let original length be x and width be y.
Case 1 : Length = x+7
Width = y-3
Area = (x+7)(y-3) = xy

$\Rightarrow$ xy -3x+7y-21 = xy

$\Rightarrow$ 3x-7y =-21....equation(1)

Case2: length = x-7
Width = y+5
Area = (x-7)(y+5) = xy

$\Rightarrow$ xy+5x-7y-35= xy

$\Rightarrow$ 5x-7y = 35....equation (2)

Solving equations 1 and 2, x = 28 m and y =15 m