Question

the perimeter of the polygon below is 105 units. find x.

Explanation:

Step1: Set up perimeter equation

The perimeter of a polygon is the sum of its side - lengths. So, $(2x - 1)+(2x + 4)+(x + 10)+2x+2x+(3x - 4)=105$.

Step2: Combine like - terms

Combine the $x$ terms: $(2x+2x+x + 2x+2x+3x)+(-1 + 4+10-4)=105$.
$12x + 9=105$.

Step3: Isolate the variable term

Subtract 9 from both sides of the equation: $12x+9 - 9=105 - 9$.
$12x=96$.

Step4: Solve for $x$

Divide both sides by 12: $\frac{12x}{12}=\frac{96}{12}$.
$x = 8$.

Answer:

$x = 8$