SOLUTION: If the width of a certain rectangle is increased by three and the length is reduced by four, we get a square with the same area as the original rectangle. Find the length and width

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: If the width of a certain rectangle is increased by three and the length is reduced by four, we get a square with the same area as the original rectangle. Find the length and width      Log On


   

Question 893073: If the width of a certain rectangle is increased by three and the length is reduced by four, we get a square with the same area as the original rectangle. Find the length and width of the original rectangle.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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If the width of a certain rectangle is increased by three and the length is reduced by four, we get a square with the same area as the original rectangle. Find the length and width of the original rectangle.
:
we can do this with one unknown
:
let x = side of the square
then
(x+4) = rectangle length
and
(x-3) = rectangle width
:
rect area = square area
(x+4)(x-3) = x^2
x^2 - 3x + 4x - 12 = x^2
subtract x^2 from both sides
x - 12 = 0
x = 12 is the side of the square
then
16 = the length of the rectangle
9 = the width
:
check 12^2 = 16 * 9