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.

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Solution

Let

B =x
L= x+7

Original Area =x × (x×7) = x^2+7x

New length = x+7-4 = x+3
New breadth = x+3

New area = (x+3)(x+3) = x^2+6x+9

THE AREAS ARE EQUAL,

x^2 + 7x = x^2 + 6x + 9
x^2 - x^2 + 7x = 6x + 9
7x - 6x = 9
x= 9cm =Breadth
x+7 = 9+7 = 16cm = Length

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