Step-by-step explanation:
[tex]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 \\ [/tex]
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.
Answer:
Length = x + 12.
Width = x - 3.
The least possible value of x for a parallelogram to exist is = 3.
Given that the area of the parallelogram is: [tex]x^2 + 9x - 36[/tex].
We factor it.
[tex]x^2 + 9x - 36\\=(x+12)(x-3)[/tex]
We know that area = length*width.
Comparing we get:
Length = x + 12.
Width = x - 3.
We know that length can not be negative.
So, x - 3 ≥ 0
or, x ≥ 3.
So the least possible value of x for a parallelogram to exist is = 3.
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