Question

Dominic is cutting a rectangular hole in his paper, from top left corner to the bottom right corner. The rectangle will be 4.5 cm long and 3.5 cm wide. which of the following is closest to the distance between the corners of the rectangle?

Answer 1

Explanation:

So initially you have a square piece of metal, 15" x 15". You cut out squares from the corners of each side with side length x.

So you'll have a sheet that looks something like this now (assuming the formatting works):

_____

__| |__

| |

|__ __|

|____|

Your original side length was 15, but it has now been reduced by x on each side, so you're now going to have a new side length of 15 - 2x

When you fold the box up, the box will have a height of just x.

So you have a base with lengths (15 - 2x) and (15 - 2x), and a height which is just x.

V = l*w*h

So

V = (15 - 2x)(15 - 2x)(x)

= 225x - 60x^2 + 4x^3

Hope this helps