Solve the problem. 20) You have 340 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle
that maximize the enclosed area.
A) 87 ft by 83 ft
B) 170 ft by 42.5 ft
C) 170 ft by 170 ft
D) 85 ft by 85 ft

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

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