Answer:
QUADRATIC FUNCTIONS AND EQUATIONS
Danielle N. asked • 11/25/17
You have 356 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area.
(Hint: Write formula for area as a quadratic function of length and use the concept of maximum value of quadratic function)
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Michael J. answered • 11/25/17
TUTOR 5 (5)
Effective High School STEM Tutor & CUNY Math Peer Leader
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Let length = x
Let width = y
Area = xy
Perimeter equation is
2(x + y) = 356
x + y = 178
Substituting the perimeter equation in the area formula,
Area = x(178 - x)
Area = -x2 + 178x
If the zeros of this quadratic are 0 and 178, then the median is where the maximum area occurs.
178 / 2 = 89
Therefore, the dimensions are
length = 89 feet
width = 178 - 89 = 89 feet
