SOLUTION: A rectangle has an area of 180 cm^2. When the length and the width are shortened by 1 cm each, the area is reduced by 27 cm^2. Find the new perimeter.

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Question 1060743: A rectangle has an area of 180 cm^2. When the length and the width are shortened by 1 cm each, the area is reduced by 27 cm^2. Find the new perimeter.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
sides are x and y
xy=180
(x-1)(y-1)=153.
xy-y-x+1=153
180-y-x+1=153
-x-y+1=-27
x+y-1=27
x+y=28
but x=180/y
so 180/y +y=28
multiply by y
180+y^2=28y
y^2-28y+180=0
(x-18)(x-10)=0
x=18, 10
if x=18, y=10
shorten each by 1 cm and 17+9=153 or 27 cm^2 less.
But the perimeter is desired, and that would be 26*2=52 cm., twice 17 plus twice 9.