Question

1. an irregular pentagon has side lengths of $(x + 3)$, $(2x - 4)$, $(4x + 5)$, $(3x - 1)$, and $x$. which simplified expression represents the pentagon’s perimeter?

a $11x - 3$
b $24x + 60$
c $11x + 3$
d $-9x + 3$

Explanation:

Step1: Recall perimeter formula

Perimeter of a polygon is the sum of all its side lengths. For a pentagon with sides \( (x + 3) \), \( (2x - 4) \), \( (4x + 5) \), \( (3x - 1) \), and \( x \), we sum these expressions.

Step2: Sum the side lengths

\[

$$\begin{align*} &(x + 3)+(2x - 4)+(4x + 5)+(3x - 1)+x\\ =&x + 3+2x - 4+4x + 5+3x - 1+x\\ =&(x + 2x + 4x + 3x + x)+(3 - 4 + 5 - 1)\\ =&11x+(3 - 4 + 5 - 1)\\ =&11x+(3 + 5 - 4 - 1)\\ =&11x+(8 - 5)\\ =&11x + 3 \end{align*}$$

\]

Answer:

C. \( 11x + 3 \)