SOLUTION: a rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 696 feet of fencing is used. Find the maximum area of the p
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Question 138606: a rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 696 feet of fencing is used. Find the maximum area of the playground Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! a rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 696 feet of fencing is used. Find the maximum area of the playground
:
Let x = length of one side
Let L = length of the adjacent side:
:
An equation with 3 sides with a length of x, and two with a length of L
3x + 2L = 696
2L = 696 - 3x
L = (348 - 1.5x); divided both sides by 2
:
Area = L*x
Substitute (348-1.5x) for L
A = x(348-1.5x)
A = 348x - 1.5x^2
:
Arrange like a quadratic
A = -1.5x^2 + 358x
:
Find the axis of symmetry, this is the value of x for max area
x = -b/(2a); in our equation a = -1.5; b = 348
x =
x =
x = +116 is dimension of x for max area
:
Find the max area; substitute 116 for x in the equation:
A = -1.5(116^2) + 348(116)
A = -1.5(13456) + 40368
A = -20184 + 40368
:
A = +20,184 sq ft is max area
:
Did I make this understandable, this fine Saturday morning?
