Question

the perimeter of the polygon below is 105 units. find x. 2x - 1 3x - 4 2x + 4 x + 10 2x 2x

Explanation:

Step1: Set up perimeter equation

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

Step2: Combine like - terms

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

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:

$x = 8$