Question 949199: Suppose that the playground area has a length of x yards and a width of y yards. The only restriction on the playground is that the area must be 324 square yards.
a.In terms of x and y, find a formula for the perimeter, P.
b.In terms of x and y, find an equation that models the area of the playground (324 square yards).
c.Combine your formula for the perimeter, P, and the equation of the area by writing a formula for the perimeter, P, in terms of x.
d.Use the formula from Part C to find the Perimeter, P, for each value of x. Include a copy of the completed table in your answer.
x
P
9
10
18
e.Among the three sets of dimensions determined by the values of x above, which set represents the playground area with the smallest perimeter?
Found 2 solutions by rothauserc, MathLover1:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! a) Perimeter(P) = 2x + 2y
b) 324 = xy
c) from b, y = 324/x, then
P = 2x + 2(324/x)
d) if x = 9, then
P = (2*9) + (2*(324/9))
P = 18 + 72 = 90 yards
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if x = 10, then
P = (2*10) + (2*(324/10))
P = 20 + 64.8 = 84.8 yards
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if x = 18, then
P = (2*18) + (2*(324/18))
P = 36 + 36 = 72 yards
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all squares are rectangles but all rectangles are not squares, therefore
72 yards is the minimum perimeter with its sides = 18 yards
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website! Suppose that the playground area has a length of  yards and a width of  yards. The only restriction on the playground is that the area must be  square yards.
the playground area is 
given:
a.
In terms of  and  , find a formula for the perimeter,  .
since  , we have
b.
In terms of and , find an equation that models the area of the playground (324 square yards).
since given
we have 
c.
Combine your formula for the perimeter, , and the equation of the  by writing a formula for the perimeter, , in terms of .
to do so, first use  and solve for
 ....now substitute this in
 =>
d.
Use the formula from Part C to find the Perimeter, , for each value of . Include a copy of the completed table in your answer.
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e.
Among the three sets of dimensions determined by the values of  above, which set represents the playground area with the smallest perimeter?
the smallest perimeter , so we can find using
set  , represents the playground area with the smallest perimeter
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