Questions: Question 14, 6.3.39-GI Part 2 of 5 A box can be formed by cutting squares out of each corner of a piece of tin and folding the "tabs" up. Suppose the piece of tin is 18 inches by 18 inches and each side of the square that is cut out has length x. Complete parts (a) through (e). (a) Write an expression for the height of the box that is constructed. The height of the box is x inches. (b) Write an expression for the dimensions of the base of the box that is constructed. The dimensions of the base of the constructed box are inches by inches.

Solution Steps

The height of the box is determined by the length of the side of the square cut out from each corner. Since each side of the square cut out has length \( x \), the height of the box is \( x \) inches.

The original piece of tin is 18 inches by 18 inches. When squares of side length \( x \) are cut out from each corner, the length and width of the base of the box are reduced by \( 2x \) (since \( x \) is cut from both sides). Therefore, the dimensions of the base of the box are: \[ (18 - 2x) \text{ inches by } (18 - 2x) \text{ inches} \]

(a) The height of the box is \( x \) inches.

(b) The dimensions of the base of the constructed box are \( (18 - 2x) \) inches by \( (18 - 2x) \) inches.

Final Answer