Math Question Relating Area Of A Box

Question

An open rectangular box with volume 6 m3 has length three times the width. Express the surface area of the box as a function of the width of the box.

I've tried the question a few times and can't find the answer. If someone could help me out it would be very much helpful.

Answer 1

v = lwh = 6m^3, h = 6/lw

l = 3w

SA = bottom plus four sides

SA = lw + 2[2l(2h)] + 2[2w + 2h]

You can substitute 3w for each l, and, you can substitute 6/lw for each h, and, finally substitute 3w for each l in 6/lw. Then you'll have everything in terms of w.