SOLUTION: 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
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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
******
if x = 10, then
P = (2*10) + (2*(324/10))
P = 20 + 64.8 = 84.8 yards
******
if x = 18, then
P = (2*18) + (2*(324/18))
P = 36 + 36 = 72 yards
******
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.
|-----
|----- -> -> ->
|----- -> -> ->
|----- -> -> ->
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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