SOLUTION: Please help! This problem makes no sense to me!! The length of a rectangle is 4 meters longer than its width. Each side of a square is 1 meter longer than the rectangle's width.

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Question 190291: Please help! This problem makes no sense to me!!
The length of a rectangle is 4 meters longer than its width. Each side of a square is 1 meter longer than the rectangle's width. The difference between the area of the rectangle and the area is 5 square meters. Find the deimensions of the rectangle and the square.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

Let w be the width of the rectangle.

Then the length of the rectangle must be w + 4

And the measure of the side of the square must be w + 1

The area of the rectangle is the length times the width, so



The area of the square is the measure of the side squared, so



The difference between these two areas is 5, so:



Distribute and collect terms:





Check: If the width of the rectangle is 3, then the length must be 3 + 4 = 7, so the area of the rectangle is 3 times 7 = 21 square meters. The side of the square must be 3 + 1 = 4 and the area of the square is 4 squared = 16. And finally, 21 - 16 = 5. Answer checks.

One thing to notice. The problem really didn't say which was larger, the rectangle or the square. But if you tried to solve it the other way, you would come up with a negative result for the value of w (verification of this is left as an exercise for the student). This result is absurd because you can't have a negative value for the measure of something. Therefore, the area of the rectangle is definitely larger than the area of the square.

John