Question

the perimeter of the polygon below is 48 units. find x.

Explanation:

Step1: Set up perimeter equation

The perimeter of a polygon is the sum of its side - lengths. So, $(2x + 2)+3x+(2x)+(x + 3)+(3x-1)=48$.

Step2: Combine like - terms

Combining the $x$ terms: $2x+3x + 2x+x+3x=11x$. Combining the constant terms: $2 + 3-1=4$. The equation becomes $11x+4 = 48$.

Step3: Isolate the variable term

Subtract 4 from both sides of the equation: $11x+4 - 4=48 - 4$, which simplifies to $11x=44$.

Step4: Solve for x

Divide both sides by 11: $\frac{11x}{11}=\frac{44}{11}$, so $x = 4$.

Answer:

$x = 4$