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
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
