SOLUTION: Task 1: Being the first grandson, your grandparents decided to give you a rectangular field for your coming wedding. If you are given 200m wires of fencing, what dimensions would y

Question 1167080: Task 1: Being the first grandson, your grandparents decided to give you a rectangular field for your coming wedding. If you are given 200m wires of fencing, what dimensions would you choose to get the maximum area?
a. List all the possible dimensions of the rectangular field.
b. Make a table of values for the possible dimensions.
c. Compute the area for each possible dimension.
d. What is the maximum area you obtained?
e. What are the dimensions of the maximum area you obtained?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Area of a rectangle:

Perimeter of a rectangle:

Solve the perimeter function for

So the area as a function of the width given a fixed perimeter is:

The graph of the Area function is a concave down parabola because of the negative coefficient on the w squared term.

The maximum area is obtained at the vertex of the parabola. The value of the independent variable (w here) at the vertex is the additive inverse of the coefficient on the first degree term divided by 2 times the coefficient on the squared term:

So the maximum area occurs when the width is equal to one-fourth of the perimeter, in other words when the length and the width are equal so that the rectangle is a square.

John

My calculator said it, I believe it, that settles it

I > Ø

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