by decreasing each dimension by 2 units, the area of a rectangle decrease from 40 square feet (on left) to 16 square feet (on the right). find the percent decrease in area
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Draw a rectangle inside a rectangle.
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Dimensions of the outer area are x and y
Area = x*y = 40 sq. ft.
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Dimensions of the inner rectangle are (x-2) and (y-2)
Area = (x-2)(y-2)
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Equations::
xy = 40 sq ft
(x-2)(y-2) = 16 sq ft
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xy -2x -2y + 4 = 16
Substitute for "xy" to get:
40 -2x -2y = 12
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2x + 2y = 28
x + y = 14
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Using x+y = 14 , substitute for "y" and solve for "x"::
xy = 40
x(14-x) = 40
14x - x^2 = 40
x^2 - 14x + 40 = 0
Factor::
(x-10)(x-4) = 0
If x = 10, y = 4
If x = 4, y = 10
