Math CentralQuandaries & Queries


Question from Linda, a student:

A rectangle has a perimeter of 38 feet & an area of 48 square feet. What are the dimensions of the rectangle?

Linda, the area of a rectangle is the length (L) times the width (W). So 48 = LW.

Also, the perimeter is the distance around the rectangle. That's 38 = L + L + W + W.

Solve the second equation for L, then use that to substitute into the first equation.
That will allow you to find the value of W (you will have to factor a quadratic for this).
Finally, use that value of W to find the value of L using either equation (both will give you the same answer).

If you want to see an example of this, see Penny's example here.

Hope this helps,
Stephen La Rocque.

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