SOLUTION: The perimeter of a rectangle is 34m , and the area of the rectangle is 72m^2 . Find the dimensions of the rectangle.

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Question 672196: The perimeter of a rectangle is 34m , and the area of the rectangle is 72m^2 . Find the dimensions of the rectangle.
Answer by neatmath(302) About Me  (Show Source):
You can put this solution on YOUR website!

This is a system of 2 equations using geometrical formulae:

P=2L%2B2W

A=L%2AW

So we have:

34=2L%2B2W and 72=L%2AW

Let's use substitution to solve this:

L=72%2FW Then,

34=2%2A%2872%2FW%29%2B2W

34=%28144%2FW%29%2B2W

34=%28144%2FW%29%2B%282W%5E2%29%2FW

34=%282W%5E2%2B144%29%2FW

34W=2W%5E2%2B144

0=2W%5E2-34W%2B144

0=w%5E2-17W%2B72

0=%28W-8%29%28W-9%29

W-8=0 or W-9=0

W=8 or W=9

So, our width can equal 8 or 9. This also means our length can also be 9 or 8, respectively.

You can easily check that these values will work.

I hope this helps! :)

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