The length of a rectangle is 3 centimeters less than its width. What are the dimensions of the rectangle if its area is 108 square​ centimeters?

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Let the width of the rectangle be ( w ) centimeters. Then the length of the rectangle is ( w - 3 ) centimeters.

The formula for the area of a rectangle is ( \text{Area} = \text{Length} \times \text{Width} ).

Given that the area is 108 square centimeters, we can set up the equation: [ (w - 3) \times w = 108 ]

Expanding and rearranging the equation, we get: [ w^2 - 3w - 108 = 0 ]

Now, we can solve this quadratic equation for ( w ) using factoring, completing the square, or the quadratic formula. Factoring, we have: [ (w - 12)(w + 9) = 0 ]

This gives us two possible solutions for ( w ):

1. ( w - 12 = 0 ) which gives ( w = 12 )
2. ( w + 9 = 0 ) which gives ( w = -9 ) (but since width cannot be negative, we discard this solution)

So, the width of the rectangle is 12 centimeters.

Substituting this value of ( w ) into the expression for the length, we find: [ \text{Length} = w - 3 = 12 - 3 = 9 ]

Therefore, the dimensions of the rectangle are: Width = 12 centimeters Length = 9 centimeters