Question

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

Explanation:

Step1: Set up perimeter equation

The perimeter of a polygon is the sum of its side - lengths. So, $(4x + 1)+(5x - 1)+(3x + 5)+(2x+2)=42$.

Step2: Combine like - terms

Combining the $x$ terms: $4x+5x + 3x+2x=14x$, and combining the constant terms: $1-1 + 5+2 = 7$. The equation becomes $14x+7 = 42$.

Step3: Isolate the variable term

Subtract 7 from both sides of the equation: $14x+7 - 7=42 - 7$, which simplifies to $14x=35$.

Step4: Solve for $x$

Divide both sides of the equation by 14: $x=\frac{35}{14}=\frac{5}{2}=2.5$.

Answer:

$x = 2.5$