SOLUTION: The base of a closed rectangular box has length equal to 3 times its width, which is w inches; its height is 6 in. less than its width. Express the surface area, S, of the box as

Algebra ->  Human-and-algebraic-language -> SOLUTION: The base of a closed rectangular box has length equal to 3 times its width, which is w inches; its height is 6 in. less than its width. Express the surface area, S, of the box as       Log On


   

Question 178772This question is from textbook
: The base of a closed rectangular box has length equal to 3 times its width, which is w inches; its height is 6 in. less than its width. Express the surface area, S, of the box as a function of w.
I've tried this several different times, but for some reason I just can't get the same answer that is in the back of the book. This question is from textbook

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First off, draw a rectangular solid on a piece of paper.
Label the sides L, W, and H.
Now calculate the surface area.
You should get contributions from the LW face of 2*LW, the LH face of 2*LH, and the WH face of 2*WH.
SA=2LW%2B2LH%2B2WH
SA=2%28LW%2BLH%2BWH%29
Now to the measurements,
Length = 3*Width=3*W, L=3W
Width = W
Height=Width-6=W-6, H=W-6
Go back to the surface area equation and substitute,
SA=2%28LW%2BLH%2BWH%29
SA=2%283W%2AW%2B3W%28W-6%29%2BW%28W-6%29%29
SA=2%283W%5E2%2B3W%5E2-18W%2BW%5E2-6W%29%29
SA=2%287W%5E2-24W%29%29
SA=14W%5E2-48W%29