A rectangle has length which is 5 cm less than twice its breadth. If the length is decreased by 5 cm and breadth is increased by 2 cm, the perimeter of the resulting rectangle will be 74 cm. Find the length and breadth of the original rectangle.

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Solution

Let b be the original breadth of the rectangle.

Then the original length of the rectangle will be

New length = 2b − 5 − 5 = 2b − 10

New breadth = b + 2

New perimeter = 74

Alternative method:

Let the length and breadth of the original rectangle be l cm and b cm respectively.

Substituting (1) in (2), we get:

From (2), we get:

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