Question 437704: A rectangular garden is 4m longer than it is wide. If the width is decreased by 1m, and the length is increased by 5m, the area is increased by 15m^2. Find the original dimensions of the garden.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A rectangular garden is 4m longer than it is wide. If the width is decreased by 1m, and the length is increased by 5m, the area is increased by 15m^2. Find the original dimensions of the garden
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let x=length of original dimension of garden
let y=width of original dimension of garden
x=y+4
y=x-4
xy=original area of garden
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x+5 = new length
y-1 = new width
(x+5)(y-1)=new area of garden
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new area-original area=15 m^2
(x+5)(y-1)-xy=15
(x+5)(x-4-1)-x(x-4)=15
(x+5)(x-5)-x^2+4x=15
x^2-25-x^2+4x=15
4x=40
X=10
y=x-4=10-4=6
ans:
original length of garden=10 m
original width of garden=6 m
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Check:
Original area=xy=6*10=60
New area=(x+5)*(y-1)=15*5=75, an increase of 15 m^2
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