A piece of tin, y = 12 inches on a side, is to have four equal squares cut from its corners, as in the illustration.If the edges are then to be folded up to make a box with a floor area of 16 square inches,
Find the depth of the box.
A) 9 in
B) 4 in
C) 8 in
D) 7 in
E) 11 in

Question

A piece of tin, y = 12 inches on a side, is to have four equal squares cut from its corners, as in the illustration.If the edges are then to be folded up to make a box with a floor area of 16 square inches,
Find the depth of the box. 
A) 9 in 
B) 4 in 
C) 8 in 
D) 7 in 
E) 11 in

Quizplus · Accepted Answer

After cutting out the squares and folding up the sides, the dimensions of the box will be:

Length = 12 - 2x (x is the length of the side of each square cut from the corners)
Width = 12 - 2x
Depth = x

We want the floor area to be 16 square inches, so:

(12 - 2x)(12 - 2x) = 16

144 - 48x + 4x^2 = 16

4x^2 - 48x + 128 = 0

Dividing by 4 gives:

x^2 - 12x + 32 = 0

Factoring gives:

(x - 4)(x - 8) = 0

So the possible values for x are 4 inches and 8 inches.

However, since the length and width of the tin are only 12 inches each, cutting squares with sides that are 8 inches long would be impossible. Therefore, the only possible value for x (and the depth of the box) is 4 inches.

Therefore, the answer is B) 4 in.

A Piece of Tin, Y = 12 Inches on a Side