SOLUTION: What is the smallest perimeter that can be used to make a rectangle with an area of 256cm squared?
Algebra.Com
Question 388350: What is the smallest perimeter that can be used to make a rectangle with an area of 256cm squared?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
What is the smallest perimeter that can be used to make a rectangle with an area of 256cm squared?
-----------------------------
Area = LW
256 = LW
W = (256/L)
-------
Perimeter = 2(L+W)
P = 2(L + (256/L))
---
P = 2(L^2+256)/L
----
Take the derivative to get:
P' = 2[(L^2+256)-L(2L)]/L^2
----
Solve: 2[(L^2+256)-L(2L)]/L^2 = 0
---
Solve: L^2+256-2L^2 = 0
-L^2 = -256
L^2 = 256
---
L = sqrt(256) = 16
Therefore W = sqrt(256) = 16
===============================
Perimeter = 4*16 = 64
===============================
Cheers,
Stan H.
RELATED QUESTIONS
Information: A rectangular box which is open at the top, has a square base with sides of... (answered by josgarithmetic)
The length of a rectangle is four times its width.
If the area of the rectangle is... (answered by JBarnum)
What is the minimum perimeter possible for a rectangle with an area or 500cm... (answered by Fombitz)
A rectangle yard with an area of 50 m squared is to be fenced on three sides. minimizing... (answered by josgarithmetic)
For a rectangle with area 324 to have the smallest perimeter, what dimensions should it... (answered by JBarnum)
Alexa drew a rectangle with an area of 36 square centimeters. The rectangle she drew... (answered by stanbon)
A square have area 256cm^2 find perimeter of... (answered by onlinepsa,ikleyn)
The perimeter is minimized for a rectangle with an area pf 35cm^2. What is the area of a... (answered by ikleyn)
What is the maximum area that can be obtained from a rectangle if the perimeter is to be... (answered by rfer)