Question

A rectangular piece of metal is 8 in. longer than it is wide. Squares with sides 3 in. long are cut from the four​ corners, and the flaps are folded upward to form an open box. Which equation indicates that the volume of the box is 76 in. cubed​?

Answer 1

Let the width be = w

The length will be = w+8

And height = 3 inches

Volume = l x w x h

`76=w(w+8)(3)`

=>
`76=(w^(2)+8w)3`

=>
`76=3w^(2)+24w`

=>
`3w^(2)+24w-76=0`

Solving this we get w = 2.43 inch or w = -10.43 inch

Neglecting the negative value, we get w = 2.43 inches.

And l=
`2.43+8=10.43` inches