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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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