Question

A box with no top is to be constructed from a piece of cardboard whose Width measures x inch
and whose length measures 3 inch more than the width

the box is to be formed by cutting squares that measure 1 inch on each side of the 4 corners and then folding up the sides

If the volume of the box is 180 inch then what are the dimensions

Now I am trying to solve it through

Volume=L * W * Height

Length = 3+x
Width = x
Height 1inc
and Volume 180 inch

AM I wrong?

Answer 1

If you make a sketch you will see that the
length = 3+x - 2 = x+1
and the width is
x-2
the height will be 1
Volume = (x+1)(x-2)(1) = 180
x^2 - x - 2 - 180 = 0
x^2 - x - 182 = 0
(x-14)(x+13) = 0
x = 14 or x = -13, but clearly x > 0

box is x+1 by x-2 by 1
or
15 by 12 by 1

check: what is 15*12*1 ?
is the length of 15 greater than the width of 12 by 3 ?

Answer 2

Thank you Reiny you are absolutely right with what you have but for some reason it does not match up to the answers in the multiple choice.

The multiple choice includes

1. 17 inch by 14 inch
2. 21 inch by 18 inch
3. 20 inch by 17 inch