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

Answer:

a) Length $x + 12$, Width $x - 3$, b) $x = 3$

Step-by-step explanation:

a) The expressions for the length and width of the parallelogram can be determined by factorizing the polynomial:

$A = x^{2} + 9\cdot x - 36$

$A = (x+12)\cdot (x-3)$

Length

$x + 12$

Width

$x - 3$

b) Since area is a positive variable, the set of solutions encompass all values of x such that area is zero o greater. Then, there are two interval where A is positive:

- When both binomials are negative.

$x \leq 3$ and $x \leq -12$

$x \leq -12$

- When both binomials are positive.

$x \geq 3$ and $x \geq -12$

$x \geq 3$

Since x is an integer, x must be positive and therefore the least possible value of x is:

$x = 3$