Question

A box that hold a pen has square ends, and its length is 13cm longer than its width. The volume of the box is 60cm^3. Determine the dimensions of the box.
How am i suppose to find the height, or any of the dimensions based on what i am given

Answer 1

The ends are square. So the width and the height are the same.
Assume the width is W
Length L = (W + 13)
Volume = Length x Width x Height = (W + 13)(W)(W) = 60
Solve for W.
Then find L.

Answer 2

How do i solve for w?

Answer 3

@ranga

Answer 4

Multiply and expand the equation:
W^2(W + 13) = 60
W^3 + 13W^2 - 60 = 0

This is a cubic equation. It has to be solved by trial and error.
Try W = 1, W = 2, W = 3, etc. and see when W^3 + 13W^2 - 60 changes sign. As soon as you see the sign change you will know there is a root (or a zero) somewhere between them. Can you tell me what you get for (W^3 + 13W^2 - 60) when you try W = 1, W = 2, W = 3?

Answer 5

Thank you so much! This totally helped me! It will help me for all my other questions too! Thank you again!

Answer 6

You are welcome. So what did you get for W and L?

Answer 7

the width and height are 2cm, and the length is 15cm!

Answer 8

Yes, you have the correct answer!

Luckily here for W = 2, (W^3 + 13W^2 - 60) goes to zero. So we know W = 2 is the solution. If the expression did not go to 0 then we have to see for between what values of W the expression changes sign (goes from positive to negative or negative to positive) and then try decimal values for W in between those points. It is good we did not have to do that here.

Answer 9

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