Question

A parallelogram has an area of x2 + 9x - 36.

a. What are expressions for the length and width of the parallelogram?
b. If x is an integer, what is the least possible value of x for a parallelogram
to exist? Explain.

Answer 1

Explanation:

Please use " ^ " to indicate exponentiation:

A = x^2 + 9x - 36. This factors into A = (x + 12)(x - 3). We can assume that the length of the parallelogram is x + 12 and that the width is x - 3.

Note that if x = 3 the area becomes zero. So: x must be greater than 3, so that the (x - 3) factor is positive.

Example: If x = 4, then the dimensions of the parallelogram are 4 + 12, or 16, and 4 - 3, or 1.