SOLUTION: using the perimeter given,find the dimensions of the rtectangle with the greatest area( I need to know the process) example p=64

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Question 732631: using the perimeter given,find the dimensions of the rtectangle with the greatest area( I need to know the process) example p=64
Answer by solver91311(24713) (Show Source):
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So

Then

Substituting to create Area as a function of width:

where

or put another way:

Note that this is a quadratic in with a negative lead coefficient so the graph is a parabola opening downward. Hence the vertex represents the value of the independent variable () that yields the maximum area ().

The coordinate of the vertex of the parabola represented by is given by , hence the value of the width that yields the maximum area for our rectangle must be:

.

I leave it as an exercise for the student to calculate the length given that the width is .

J0ohn

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it