SOLUTION: using the perimeter given,find the dimensions of the rtectangle with the greatest area( I need to know the process) example p=64
Algebra.Com
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): You can put this solution on YOUR website!
So
Then
Substituting to create Area as a function of width:
\ =\ \frac{Pw\ -\ 2w^2}{2}\ \ )
where 
or put another way:
\ =\ -w^2\ +\ \frac{P}{2}w)
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 \ =\ a^2\ +\ bx\ +\ c)
is given by 
, hence the value of the width that yields the maximum area for our rectangle must be:
}\ =\ \frac{P}{4})
.
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
RELATED QUESTIONS
Using whole units and the perimeter given, find the dimensions of the rectangle with the (answered by ewatrrr)
Find the dimensions of a rectangle (a) with the greatest area whose perimeter is 30... (answered by Alan3354)
Using the perimeter given, find the dimensions of the rectangle with the greatest area... (answered by Alan3354)
A=64 using each area measurement given, find the dimensions of the rectangle with the... (answered by lynnlo)
can someone help me,i dont get this!!! Find the dimensions of a rectangle a with the... (answered by mathispowerful,scott8148)
Find the dimensions of the rectangle of greatest area whose perimeter is 20... (answered by drk)
Id need help here please, find the dimensions of a rectangle "a" with the greatest area... (answered by jim_thompson5910)
Find the dimensions of a rectangle of greatest area which has a fixed perimeter... (answered by Alan3354)
find the dimensions of a rectangle "a" with the greatest area whose perimetter is 30... (answered by stanbon,solver91311)
