A rectangle is 8cm longer than it is wide. IF its length and width are both decreased by 2cm, its area is decreased by 108cm^2 . Find its original dimensions

Question

Area Problems

Answer 1

Let the width of the original rectangle be x cm. Then, the original length of the rectangle is x + 8 cm. Area of a rectangle is length times width, so in terms of x:

Original Area = x² + 8x

If the length and width are both decreased by 2 cm, the new dimensions become:

1. New width: x − 2
2. New length: x + 6

Therefore, the new area in terms of x:

New Area = x² + 4x − 12

According to the problem, the decrease in area is 108 cm²:

Original Area − New Area = 108

(x² + 8x) - (x² + 4x − 12) = 108

Solving for x, you get x = 24, which is the original width of the rectangle. The original length of the rectangle is (24) + 8 = 32.

Original width: 24 cm

Original length: 32 cm

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