SOLUTION: the area of a rectangular playground is 160 sq.m. and its perimeter is 52sq.m. what is the length and width of the playground? please help...please also show the solution so i w

Question 205954: the area of a rectangular playground is 160 sq.m. and its perimeter is 52sq.m. what is the length and width of the playground?
please help...please also show the solution so i will know how to solve...thanks
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
Area = Length * Width,,A=LW = 160,,,,,,,or L=160/W
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Perimeter = 2(L+W) ,,,,,P=2L +2W =52,,,,subst from above
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52= 2(160/W) +2W,,,,,multiply thru by "W"
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52W = 320 +2W^2
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2w^2 -52W +320 =0,,,,,divide by 2
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W^2 -26W +160 =0
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solve for W,,,using Quadratic Formula
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a=1,,,,b=(-26),,,c=160
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W=[ -(-26) +/-sqrt{ (-26)^2 -4 (1)(160)}]/2(1)
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W= [26 +/- sqrt{676 -640}]/2
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W= [26 +/- 6]/2
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w= 10,,16
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solving for L=160/W,,,L= 16,10
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Therefore,,,W=10,,,L=16,,,,,,by convention W less than L
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Check, A= 10*16=160,,,ok
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P=2(10+16)=2*26 = 52,,,,,ok
.

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