Question 257156: A rectangular field with area 5000 meters squared is enclosed by 300 meters of fencing. Find the dimensions of the field.
Answer by unlockmath(1688)   (Show Source):
You can put this solution on YOUR website! Hello,
Let's set up 2 equations and work from that. x will be one side and y the other side.
x*y=5000 sq meters
2x+2y=300 meters
Lets' work the first equation so"
x=5000/y Now plug this into the second equation to give us:
2(5000/y)+2y=300 rewritten it will be:
10000/y+2y=300 Multiply by "y" to be:
10000+2y^2=300y Subtract 300y from both sides:
2y^2-300y+10000=0 Pull 2 out from this:
2(y^2-150+5000)=0 Factor this to be:
2(y-50)(y-100)=0 we have 2 solutions:
y=50
y=100 Now plug these into the first equation and we'll have:
x=100
x=50
This works out that one side is 50 meters and the other side is 100 meters.
From this we can figure out the perimeter and area which is 300 meters around and 5000 square meters for the area.
Good problem!
Make sense?
RJ
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www.math-unlock.com
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