Question

A parallelogram has an area of x^2 + 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.Please help! ​

Answer 1

Step-by-step explanation:

$Area \: of \: parallelogram \\ = {x}^{2} + 9x - 36 \\ = {x}^{2} + 12x - 3x - 36 \\ = x(x + 12) - 3(x + 12) \\ = (x + 12)(x - 3) \\ \implies \\ length = (x + 12) \: units \\ width = (x - 3) \: units$

For this parallelogram to exist least value of x should be 4.

Because if x = 3

(x - 3)= 3 - 3 =0

Thus width of parallelogram would become zero as a result area of parallelogram would become zero i. e. Parallelogram won't exist.