Question

Squares of side x are cut from each corner of an 8 inches x 5 inch in rectangle, so that its sides can be folded to make a box with no top. define a function in terms of x that can represent the area of the base of the box

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Answer 1

When we do not have anything cut of the rectangle, the area is:

8in*5in = 40in^2.

Now, when we cut squares of length x in the corners, the measures of the base will be:

8in - 2*x

5in - 2*x

We subtract two times x in each case because we cut the squares in the four corners. (below you can see a drawing of this situation, where the doted rectangle is the area that we want to calculate)

Then the area as a function of x is:

A = (8in - 2*x)(5in - 2*x) = 40in^2 + 4*x^2 - 26*x