SOLUTION: the area of a rectangular field is 1200 m^2. two parallel sides are fenced with aluminum at $20/m. the remaining two sides are fenced with steel at $10/m. the total cost is $2200

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: the area of a rectangular field is 1200 m^2. two parallel sides are fenced with aluminum at $20/m. the remaining two sides are fenced with steel at $10/m. the total cost is $2200       Log On


   

Question 135538: the area of a rectangular field is 1200 m^2. two parallel sides are fenced with aluminum at $20/m. the remaining two sides are fenced with steel at $10/m. the total cost is $2200
a. what is the length of each side fenced with aluminum?
b. what is the length of each side fenced with steel?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the length of a side fenced with aluminum a
Call the length of a side fenced with steel s
a%2As+=+1200 m2
The total length of aluminum fence = 2a
The total length of steel fence = 2s
20%2A%282a%29+%2B+10%2A%282s%29+=+2200
40a+%2B+20s+=+2200
s+=+1200%2Fa
40a+%2B+20%2A%281200%2Fa%29+=+2200
40a%5E2+%2B+24000+=+2200a
a%5E2+-+55a+%2B+600+=+0
Use the quadratic formuala
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+-55
c+=+600
x+=+%28-%28-55%29+%2B-+sqrt%28+%28-55%29%5E2-4%2A1%2A600+%29%29%2F%282%2A1%29+
x+=+%2855+%2B-+sqrt%28+3025+-+2400+%29%29%2F2+
x+=+%2855+%2B-+sqrt%28+625+%29%29%2F2+
x+=+%2855+%2B-+25%29%2F2+
x+=+40
x+=+15
If a+=+40, then s+=+1200%2Fa and
s+=+30
40a+%2B+20s+=+2200
40%2A40+%2B+20%2A30+=+2200
1600+%2B+600+=+2200
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If a+=+15, then
s+=+80
40a+%2B+20s+=+2200
40%2A15+%2B+20%2A80+=+2200
600+%2B+1600+=+2200
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The length of each side fenced with aluminum can be 40 m and the
length of a side fenced with steel will be 30 m
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The length of the side fenced with aluminum can also be 15 m and
the length of a side fenced with steel will be 80 m