SOLUTION: Rectangle R has varying length l and width w but with a constant perimeter of 4 feet. a)Express the area A as a function of length l Write a list of everything you know about thi

Question 894736: Rectangle R has varying length l and width w but with a constant perimeter of 4 feet.
a)Express the area A as a function of length l
Write a list of everything you know about this function.
b)For what values of land w will the area of R be the greatest?
Give an algebraic explanation. Then give a geometric explanation. Be sure to include a graph with relevant points labeled.

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Length is L, width is w.

, and , the constant perimeter of 4 feet.
Simplify perimeter equation to .

Part (a) asks for A(L).
from perimeter equation, w=2-L.

Or if you want,
, area as a function of length.

The function A(L) is quadratic, and has a maximum value, based on coefficient on being .

The maximum value for area will be at L=w, meaning a square shape. This will simply be L=1 and w=1; and the area will be 1 square foot.

Part (b): you asked for an algebraic explanation but I did not give it that way. I simply gave a discussion.

Try this:
Find roots for A(L).

or .
The maximum value occurs in the exact middle of these roots.
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