Question

1. the perimeter of the polygon below is 44 units. find x.

Explanation:

Step1: Set up perimeter equation

The perimeter of a polygon is the sum of its side - lengths. So, $7+(x + 5)+9+(3x-1)=44$.

Step2: Combine like - terms

First, combine the constant terms: $7 + 5+9-1=20$, and the $x$ terms: $x+3x = 4x$. The equation becomes $4x+20 = 44$.

Step3: Isolate the variable term

Subtract 20 from both sides of the equation: $4x+20-20=44 - 20$, which simplifies to $4x=24$.

Step4: Solve for $x$

Divide both sides of the equation by 4: $\frac{4x}{4}=\frac{24}{4}$, so $x = 6$.

Answer:

$x = 6$