Question

In a rectangular piece of cardboard with a perimeter of 20ft, three parallel and equally spaces creases are made (so the piece is divided into four equal sections.) The cardboard is then folded to make a rectangular box with open square ends.

a. Write a formula for the volume of the box.

b. Find the domain of a.

Answer 1

.................
. . . . .
. . . . .
. . . . . y
. . . . .
.................
------4x-------

let the length of the original rectangle be 4x (so that each of the smaller rectangles is x )
let the width be y

After it is folded, the volume would be
y(x^2)
but 8x + 2y = 20
or y = 10 - 4x

so Volume = (10 - 4x)x^2

for b. you ask "what is the domain of a"

there is no a

Answer 2

looks like my diagram did not come out correctly.
It was supposed to be a large rectangle 4x by y, divided into 4 equal rectangles each x by y

Answer 3

(-1,4)(5,8) into general equation form