Write a function A representing the area I the base of the box in terms of x.

Question

You use a rectangular piece of cardboard measuring 20 in. by 30 in. to construct a box. You cut squares with sides x in. from each corner of the piece of cardboard and then cold up the sides to form the bottom. Write a function A representing the area I the base of the box in terms of x.

Answer 1

When you cut a square of side x from each corner, it reduces the length and width by 2x.  Hence the area, A(x), of the bottom of the box will be:

 

A(x) = (30-2x)(20-2x) = 4x² - 100x + 600