Question

PLEASE HELP!!! Pr-Cal Question 20 points

A farmer has 120 feet of fencing available to build a rectangular pen for her pygmy goats. She wants to give them as much room as possible to run. What are the dimensions of the rectangular pen with the largest area?
Write an expression in terms of a single variable that would represent the area of a rectangle in this family.

Please show your work.

Answer 1

Answer:

3600

Step-by-step explanation:

perimeter is  120ft

Goal is to get the largest area.

so you can start with a list of possible solutions:

1*119 = 119ft

2*118 = 236ft

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.

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60*60 =3600ft

61*59 = 3599ft

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Answer 2

Answer: it is well known that the largest area would be a circle with circumference 120 ft, and it is well known that a square 30ft on a side gives the most area of all retangles with perimeter 120 ft, but we are to prove it. The equation is area = side × (60 - side).

Step-by-step explanation:

Let s be one side of the rectangle, and 60-s be the other side. Maximize the area, which is

a(s) = s×(60-s) = -s^2 + 60s

This quadratic equation reaches a maximum when da(s)/ds = 60 - 2s = 0.

2s = 60, s = 30.