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 Question from Ivan, a student: The length of a rectangle is 31 centimeters less than five times its width. Its area is 72 sq centimeters. Find the dimensions of the rectangle.

Hi Ivan,

You are asked for the dimensions of the rectangle and the dimensions are the length and the width so let's call the length $L$ centimeters and the width $W$ centimeters. You are told that the area is 72 square centimeters so

$L \times W = 72.$

Now read the first sentence carefully "The length of a rectangle is 31 centimeters less than five times its width." Five times the width is $5 \times W$ and 13 centimeters less than this is $5\times W - 13.$ You are told that this is the length so

$L = 5\times W - 13.$

Substitute this for $L$ in the first equation and solve fro $W.$ Once you know the width you can use the fact that the area is 72 square centimeters to find the length.

Penny

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