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laila [671]
3 years ago
7

PLEASE HELP!!! Pr-Cal Question 20 points

Mathematics
2 answers:
Brilliant_brown [7]3 years ago
7 0

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

.

.

.


60*60 =3600ft

61*59 = 3599ft

.

.


Irina18 [472]3 years ago
4 0

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.

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