Question

there is a box that has a volume of 120 cubic inches. it is 2 inches thick and must have a 184 surface area. (there is no top to this box) what are the dimensions of the box please explain how you got there

Answer 1

V=LWH
W=2
120=V
120=L2H
divide by 2
60=LH

SA
2 pairs of same sides
1 bottom

SA=2(LH+WH)+LW
we know that W=2 so
SA=2(LH+2H)+2L
exanded
SA=2LH+4H+2L

we need to solve for 1 variable to eliminate it
60=LH
divide both sides by L
60/L=H
sub 60/L for H

SA=2L(60/L)+4(60/L)+2L
SA=2(60)+(240/L)+2L
SA=120+(240/L)+2L
SA=184
184=120+(240/L)+2L
multiply both sides by L
184L=120L+240+2L²
minus 184L both sides
0=2L²-64L+240
factor
0=2(L²-32L+120)
use quadratic formula
L=16-2√34 or 16+2√34

the dimentions are (aprox)
Legnth=4.3381, Width=2, Height=13.831 or
Legnth=27.6619, Width=2, Height=2.1691