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Let the length be a and the width be a-5:

a*(a-5) = 24

a2-5a =24

a2-5a-24 = 0

Solving the above quadratic equation works out as:

a = -3 or a = 8 it must be the latter because dimensions can't be negative.

Answer: length = 8 cm and width = 3 cm

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Q: The rectangle has an area of 24 square centimeters. Find the length of a of the rectangle. The two sides are a and a-5.?
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