Math CentralQuandaries & Queries


Question from Shawn, a student:

The width of a rectangle is 4 less than twice its length. If the area of the rectangle is 72 cm,
what is the length of the diagonal

Hi Shawn.

The area of a rectangle is length x width. If the length is L, then the width is W = 2L - 4 (that's "4 less than twice the length"). So the area is L x (2L -4).

L (2L - 4) = 72 cm2

Solve for L using factoring, the quadratic formula or completing the square.

Now solve for the width using W = 2L - 4.

Finally, use the Pythagorean theorem to calculate the length of the diagonal.

[ Note: with these numbers, things don't work out "nicely" or evenly. That's okay mathematically, but check the original question and make sure you copied the numbers down right before you do the calculation

Stephen La Rocque.

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