A rectangle is 12 cm longer than it is wide. If its length and width are both decreased by 2 cm, its area is decreased by 108 cm². Find its original dimensions.

Let the width be "x" cm.

Then the length is "x+12" cm

And the area = x(x+12) = x^2+12x cm^2

Change the dimensions:

width = "x-2" cm

length = "x+10" cm

New area = (x-2)(x+10) = x^2 + 8x - 20 cm^2

Equations :

Old area - New area = 108 cm^2

x^2+12x -(x^2 + 8x - 20) = 108

4x + 20 = 108

4x = 88

x = 22 cm (original width)

x+12 = 24 cm (original length)

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