The length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the original rectangle. Find the length and the breadth of the original rectangle.

Let the length and breadth of a rectangle be l cm and b cm


According to the question


l - 7 = b (A)


Area of a rectangle = (l × b)


And (l - 4)(b + 3) = lb


Putting (A) we get


(l - 4)(l - 7 + 3) = l(l - 7)


By cross multiplication


l2 - 4l - 4l + 16 = l2 - 7l


l2 - l - 8l + 7l = - 16


- l = - 16


l = 16 cm


b = l - 7 = 16 - 7 = 9 cm


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