Question

A rectangular piece of sheet metal has a length that is 10 10 in. less than twice the width. A square piece 5 5 in. on a side is cut from each corner. The sides are then turned up to form an uncovered box of volume 1210 1210 in. cubed in.3 Find the length and width of the original piece of metal.

Answer 1

• length: 32 in
• width: 21 in

Explanation:

If the width of the original piece of sheet metal is x, then the length is 2x-10. Subtracting a 5" square from each corner makes the bottom of the box have dimensions (x-10) and (2x-20). The volume of the box is then ...

5(x -10)(2x -20) = 1210 . . . . . . volume is the product of the dimensions

10(x -10)² = 1210 = 10(11²) . . . . factor the equation

(x -10)² = 11² . . . . . . . . divide by 10

x = 11 + 10 = 21 . . . . . .take the square root, add 10

The length and width of the original piece of sheet metal were 32 inches and 21 inches, respectively.