Question

A carpenter is building a rectangular room with a fixed perimeter of 376 ft. What dimensions would yield the maximum area? What is the maximum area?

Answer 1

2l+2w=376
lw=a

these are the 2 equations u need
differentiate the area in terms of length so u need to solve for w in the first equation then substitute into second equation. after that differentiate the equation u substituted to and set it equal to 0

Answer 2

l = w = 94

Answer 3

376/4=94

94^2=8836

Answer 4

also when perimeter is limited and u have to choose between a rectangle and a square, a square holds more area.