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?

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 ?

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

No, you are on the right track! Let's go through the problem step by step to find the correct solution.

First, let's start by finding the dimensions of the box. The length of the box is given as 3 inches more than the width, so we can say:

Length = Width + 3

Next, we know that four squares measuring 1 inch on each side are cut from the corners of the cardboard. When the cardboard is folded into a box, these squares will become the height of the box.

So the height of the box is 1 inch.

Finally, we are given that the volume of the box is 180 inches. Using the formula for calculating volume, which is Length * Width * Height, we can substitute the known values and solve for the unknowns.

Volume = Length * Width * Height
180 = (Width + 3) * Width * 1

Simplifying the equation, we have:

180 = Width^2 + 3Width

Now, to find the dimensions, we need to solve this quadratic equation.

To do that, we can rearrange the equation to be in the form of:

Width^2 + 3Width - 180 = 0

We can now use factoring, completing the square, or the quadratic formula to solve for Width. Once we find the value of Width, we can substitute it back into the equation Length = Width + 3 to find the length.

Solving the quadratic equation, we find that the width of the box is approximately 12 inches.

Substituting this value back into the equation Length = Width + 3, we can calculate the length as:

Length = 12 + 3 = 15 inches.

So, the dimensions of the box that satisfies the given conditions and has a volume of 180 inches are: Width = 12 inches, Length = 15 inches.