in algebra-what is the largest perimeter of a rectangle if the area is 36?

Question

this is for my algebra class

Answer 1

There is no limit to the perimeter you can achieve. Example:

Length = 36,000,000

Width = 1/1,000,000

L*W = 36.

So you can make length arbitrarily large, as long as you make the rectangle "skinny enough."

Answer 2

There is no largest perimeter for a rectangle of area 36 because given any N>0, I can construct a rectangle with side N and side 36/N. Then the perimeter = 2N + 2*(36/N) > 2N.

Picking N arbitrarily large shows that the perimeter can be made arbitrarily large.

Answer 3

First class eh? the largest perimeter? I thought it would be the smallest perimeter.
Well the smallest is a square so S^2 = 36 and the side is 6.
The perimter is then 4S = 24

I thought you had used the wrong word but others are taking the problem at face value and it is true that there is no largest perimeter.
p = 2w + 2l
l = (p - 2w)/2
area = wl = w(p - 2w)/2 = 36
36 = (wp - 2w^2)/2
so p = (72 + 2w^2)/w = 72/w + 2w which goes to infinity as w gets smaller and smaller. So there is no largest perimeter

Answer 4

GI is right. However I obtained an algebraic formula.
L * W = 36
so therefore, L = 36 / W
W = 36 / L

Perimeter = 2 (L + W)
= 2 ( (36 / W) + (36 / L) )
= 2 ( (36 (L+W)) / LW)

Answer 5

74, because the length is 36 and width is 1= (36x2)+(1x2)=74
2 and 18 won't work, 3 and 12 won't work, 4 and 9 won't work, and 6 and 6 won't work

Answer 6

74

a 36x1 rectangle

bored to show solution...