word problem

Question

A square piece of tin, 14 inches on a side, is to have four equal squares cut from its corners, as shown. If the edges are then to be folded up to make a box with a floor area of 36 square inches, find the depth of the box.

Answer 1

Charles,

 

The picture is VERY IMPORTANT in understanding this problem.  Look at it closely.  It has all the information that you need to solve this problem, so get used to understanding figures (and drawing them if they are not already there).

 

I'll imagine a big square and four smaller squares cut out of the corners such that the four sides fold upward to make a square box (I've made such boxes recently to mail books back for resale).

 

The problem states that the floor area becomes 36 square inches, which for a square happens when each side is 6 inches.

 

That leaves a total of 8 inches out of the original 14 inches on each side that would be cut out.  Yep, 4 inches on each side of the small squares.  When folded up, these four inches are the depth of the box.  Note: the top of the box is open, so I couldn't use this box for mailing books (also, it is tin).

Answer 2

Let x = length of a square corner

 

The box will have depth x and the bottom of the box will be a square 14 - 2x inches per side

 

So, (14 - 2x)² = 36

 

14 - 2x = 6

 

-2x= -8

 

x = 4"