Box volume problem: square cut from corners, and polynomial equation

[mustang]

Problem 5.
An open box with a volume of 144cm^3 can be made by cutting a square of the same size from each corner of a square piece of tin 14cm on a side and folding up the edges of the tin. What is the length of a side of the square that is cut from each corner?

Problem 24. Slove.
f(x)=2x^3+9x^2+x-12

 

[Parth Dave]

V = lwh
square piece of tin implies that length = width
l = (14-z) where z is the amount cut
V = h(14-z)^2
144 = h(14-z)^2

unless I am missing something, you have 2 variables and one equation.. i don't think you can solve it..

 

[HallsofIvy]

The height of the box IS z: when you fold the cut part up to form the sides, their height is the same as the length cut out:

144= z(14-z)².

 

[Parth Dave]

ah right, my mistake.