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| Math Central | Quandaries & Queries |
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Question from Charlene, a student: The area of a rectangle is 390m^2. If its length is increased by 10m and its width is decreased by 6m, then its area does not change. Find the perimeter of the original rectangle. |
Hello,
Let x be the length, and y be the width of the rectangle.
The area and perimeter of the rectangle are:
Area = x · y Perimeter = 2x + 2y
We are given that the area is 390 metres square and remains the same if the length is increased by 10 and the width decreased by 6, thus:
x · y = 390 (x + 10)(y - 6) = 390
Therefore
x · y = (x + 10)(y - 6)
x · y = x · y - 6x + 10y - 60
60 = - 6x + 10y
y = (60 + 6x)/10
And we have a value to substitute back into our first equation,
390 = x (60 + 6x)/10
Solve for x , and then for y , then determine perimeter.
Tyler
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