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Answer :
Maximize the enclosed area of the rectangle is 85 ft by 85 ft.
What is perimeter of rectangle?
Perimeter of rectangle is defined as addition the lengths of the rectangle's four sides.
Let length = a
Let width = b
Area of rectangle = ab
Perimeter of rectangle equation is 2(a + b)
2(a + b) = 340
a + b = 170
Substitute the perimeter equation in the area formula,
Area = a(170 - a)
Area = -a² + 170a
If the zeros of this quadratic are 0 and 170, then the median is where the maximum area occurs.
170 / 2 = 85
Therefore, the dimensions are
length = 85 feet
width = 170 - 85 = 85 feet
The rectangle is a square.
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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
