question help (1 Viewer)

[ibrian]

a square piece of sheet metal has a side length of 12m. A square of length ' x' m is to be cut from each corner of the sheet metal and the sides bent up to form an open rectangular prism
*A) what is the maximum possible value of x ?
*B) show that the volume of the prism formed can be given by the function V= x(12-2x)^2

edit: only need part A, done part B

thanks

 

[PC]

Since the total side length is 12 metres, and sides are bent up from both ends, the length and width of the box produced will be (12 – 2x) metres, and the height is x metres.

Now the length and width must give a positive number, so:
12 – 2x > 0
–2x > – 12
x < 6

Or, in other words, x can't be any bigger than 6. If x = 6 then you won't actually get a box, so we need x to be less than 6.