Math CentralQuandaries & Queries


Question from Josh, a student:

Dave and Jane have a new rectangular driveway. The perimeter of the driveway is 168 feet. The length is 12 feet longer than three times the width. What are the dimensions of the driveway?


Suppose the length of the driveway is L feet and the width is W feet. The perimeter is 168 feet so walking around the driveway and measuring the sides gives

L + W + L + W = 168 feet.

or just going half way around

L + W = 84.

This can be rewritten

L = 84 - W.

Now look at the sentence "The length is 12 feet longer than three times the width." If the width is W feet what is 3 times the width? What is 12 feet more than three times the width? This is the length so now you have a second expression for L. Set the two expressions equal to each other and solve for W.

I hope this helps,

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