SOLUTION: The length of a rectangle is three times its width. If the width is decreased by 1 meter and the length is increased by 3 meters, the area will be 72 square meters. Find the dimens

Algebra ->  Rectangles -> SOLUTION: The length of a rectangle is three times its width. If the width is decreased by 1 meter and the length is increased by 3 meters, the area will be 72 square meters. Find the dimens      Log On


   

Question 844440: The length of a rectangle is three times its width. If the width is decreased by 1 meter and the length is increased by 3 meters, the area will be 72 square meters. Find the dimensions of the original rectangle.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
ORIGINAL

y length, x width
y=3x
A for area, A=xy, A=x%2A3x, A=3x%5E2

CHANGED

Length becomes y+3, and width becomes x-1;
The changed rectangle area, %28x-1%29%28y%2B3%29=72.
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xy-y%2B3x-3=72
The analysis in "Original" shows that xy=A=3x^2, so we can substitute that here.
3x%5E2-y%2B3x-3=72
The analysis in "Original" also shows that y=3x, so we can substitute for y.
3x%5E2-3x%2B3x-3=72, extremely neat since the changed equation already contains a 3x term.
3x%5E2-3x%2B3x-3%2B3=72%2B3
3x%5E2%2B3x-3x=75
3x%5E2=75
x%5E2=75%2F3=25
highlight%28x=5%29-------Width of the original rectangle.
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y=3x=3%2A5=15; highlight%28y=15%29-------Length of original rectangle.