SOLUTION: A rectangle is 3 meters longer than it is wide. If the width of the rectangle is doubled and the length is decreased by 4 meters, the area is unchanged. Find original length and wi

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Question 742776: A rectangle is 3 meters longer than it is wide. If the width of the rectangle is doubled and the length is decreased by 4 meters, the area is unchanged. Find original length and width
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
l=w+3 so
A=lw=%28w%2B3%29%28w%29=w%5E2%2B3w

After w is doubled and length is decreased by 4,
A=%28w%2B3-4%29%282w%29=%28w-1%29%282w%29=2w%5E2-2w
Now since the area has not changed
w%5E2%2B3w+=+2w%5E2-2w
w%5E2-w%5E2%2B3w-3w+=+2w%5E2-w%5E2-2w-3w
w%5E2-5w=0
w%28w-5%29=0
So width is 0 or 5m
We can discard the 0 solution.
Length is w+3, so length is 8m