Question

the perimeter of the polygon below is 42 units. find x. 4x + 1 5x - 1 3x + 5 8x - 3

Explanation:

Step1: Set up perimeter equation

The perimeter of a polygon is the sum of its side - lengths. So, $(4x + 1)+(5x - 1)+(3x + 5)+(8x - 3)=42$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $(4x+5x + 3x+8x)+(1 - 1+5 - 3)=42$, which simplifies to $20x + 2=42$.

Step3: Isolate the variable term

Subtract 2 from both sides of the equation: $20x+2 - 2=42 - 2$, resulting in $20x=40$.

Step4: Solve for $x$

Divide both sides by 20: $\frac{20x}{20}=\frac{40}{20}$, so $x = 2$.

Answer:

$x = 2$