Question

Can someone walk me through this question, step by step?
A certain rectangular box has a volume of 144 cubic inches, a surface of 192 square inches, and a height one inch greater than its width. What is the distance from one corner of the box to the diagonally opposite corner?

Answer 1

So far I know that hlw=144 and that 2hl+2lw+hw=192 and that h=w+1....

Answer 2

I'm having trouble working it out from that information, even though I think it should be enough?

Answer 3

width \(\rm w\),
height one inch greater than width, \(\rm h=(w+1)\),
length \(\rm \ell\).

Volume information:\[\large\rm 144=\ell w h\]Substituting in our height,\[\large\rm \color{orangered}{144=\ell w (w+1)}\]

Surface Area information:\[\large\rm 192=2h\ell+2\ell w+h w\]Again, substituting in our height,\[\large\rm \color{orangered}{192=2(w+1)\ell+2\ell w+(w+1) w}\]

So what we have is two equations (in orange), each of which involve two unknowns.
Hmm, so maybe we can do something with that.

Answer 4

Hmm

Answer 5

That's where I'm stuck - blanking on what to do next?

Answer 6

Ya, hmm...
Le's draw a diagram, maybe it will help make something click.