Question

Find the dimensions of the rectangle of maximum area that can be formed from a
40-in.
piece of wire

Answer 1

20 X 2

Answer 2

i already tried that it is incorrect

Answer 3

5 X 8

Answer 4

yep!!!!!

Answer 5

the perimeter is 40 inches\[l+l+w+w = 40 \implies 2l+2w = 40\]
now we can solve for either width or length, so solving for length gives us \[l = \frac{ 40-2w }{ 2 }\]using this information we can find the area of a rectangle since we know area of a rectangle is just \[A = length \times width \]\[A = l \times w\] so plugging our length into the area formula we have \[A = (20-w)w = 20w-w^2\] I simplified the length by dividing by 2 from the initial length formula I made. So now to find the maximum area, we need to take the derivative, I leave the rest to you.