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

Combining the $x$ terms: $4x+5x + 3x+8x=20x$, and combining the constant terms: $1-1 + 5-3=2$. The equation becomes $20x+2 = 42$.

Step3: Isolate the variable term

Subtract 2 from both sides of the equation: $20x+2-2=42 - 2$, which simplifies to $20x=40$.

Step4: Solve for x

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

Answer:

$2$