Question 858174: A rectangular field is 4 times as long as it is wide. If the length is decreased by 10 feet and the width is increased by 2 feet, the perimeter will be 80 feet. Find the dimensions of the original field The original dimensions are feet long by feet wide.
Answer by JulietG(1812)   (Show Source):
You can put this solution on YOUR website! L = 4W [A rectangular field is 4 times as long as it is wide.]
2(L-10) + 2(W+2) = 80 [If the length is decreased by 10 feet and the width is increased by 2 feet, the perimeter will be 80 feet. ]
Distributed: (2L - 20) + (2W + 4) = 80
Substitute the known value of L from the first equation into the second.
8W - 20 + 2W + 4 = 80
10 W -16 = 80
Add 16 to each side
10W = 96
Divide each side by 10
W = 9.6 <<--original dimension
L = 9.6 * 4 = 38.4 <<--original dimension
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That's a pretty strange answer. Let's plug it in to make certain.
If the length (38.4) is decreased by 10 feet (which would make it 28.4) and the width (9.6) is increased by 2 feet (11.6), the perimeter will be 80 feet.
28.4 + 28.4 + 11.6 + 11.6 = 80 feet.
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So, strange, but correct :-)
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