SOLUTION: The perimeter of a rectangle window is 32 ft. Find the dimension of the window that will enclose the largest area.

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The perimeter of a rectangle window is 32 ft. Find the dimension of the window that will enclose the largest area.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 33414: The perimeter of a rectangle window is 32 ft. Find the dimension of the window that will enclose the largest area.
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Perimeter is 2w+2L=32
sOLVE FOR L
l=16-w (subsistuion)
Max Area is A:
(w)(l)=A
Subsitute for l:
(w)(16-w)=A
-w^2+16w=A
Differentate with respect to w:
dA%2Fdt=%28-2w%29dw%2Fdt%2B%2816%29dw%2Fdt
-2w=-16
w=8
l=16-8
l=8
8^2=64
Hence, the largest area you can have is 64ft^2 with length of 8ft and width of 8ft.
Paul.