SOLUTION: If one side of a square is doubled in length and the adjacent side is decreased by two centimeters, the area of the resulting rectangle is 96 square centimeters larger than that o

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Question 505171: If one side of a square is doubled in length and the adjacent side is decreased by two centimeters, the area of the resulting rectangle is 96 square centimeters larger than that of the original square. Find the dimensions of the rectangle?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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If one side of a square is doubled in length and the adjacent side is decreased by two centimeters, the area of the resulting rectangle is 96 square centimeters larger than that of the original square.
Find the dimensions of the rectangle?
:
let x = the side of the square
then
x^2 = the area of the square
:
2x = length of the rectangle
(x-2) = width of the rectangle
then
2x(x-2) = 2x^2 - 4x = the area of the rectangle
:
Rect area - square area = 96 sq/cm
2x^2 - 4x - x^2 = 96
Forms a quadratic equation
x^2 - 4x - 96 = 0
factors to
(x-12)(x+8) = 0
positive solution
x = 12 cm is the side of the square
then
2(12) = 24 cm is the length of the rect
and
12-2 = 10 cm is the width of the rect
;
:
:
Check this
24*10 - 12^2 =
240 - 144 = 96 sq/cm difference