Question

A rectangular piece of metal is 20 in longer than it is wide. Squares with sides 4 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 1536 incubed​, what were the original dimensions of the piece of​ metal?

Answer 1

To find the original dimensions of the metal, subtract twice the length of each side of the square from the length and width of the box. Use the equation (w + 20 - 2(4))(w - 2(4))h = 1536 to determine the original dimensions.

Step-by-step explanation:

To find the original dimensions of the metal, we can start by determining the dimensions of the open box that is formed. Given that squares with sides 4 inches long are cut from the four corners, the length and width of the box will be the original dimensions of the metal minus twice the length of each side of the square.

Let's assume the width of the metal is 'w' inches. This means the length of the metal is 'w + 20' inches. After the squares are cut, the length and width of the box will be 'w + 20 - 2(4)' and 'w - 2(4)' inches respectively. Given that the volume of the box is 1536 in³, we can now set up the equation:

(w + 20 - 2(4))(w - 2(4))h = 1536