Question

geometry find the perimeter of the regular polygon. 5 - 2x -4x + 9 the perimeter of the polygon is units.

Explanation:

Step1: Set side - lengths equal

Since it's a regular triangle, all sides are equal. So, $5 - 2x=-4x + 9$.
Solve for $x$:
\[

$$\begin{align*} -2x+4x&=9 - 5\\ 2x&=4\\ x&=2 \end{align*}$$

\]

Step2: Find side - length

Substitute $x = 2$ into either side - length expression. Let's use $5-2x$.
$5-2\times2=5 - 4=1$

Step3: Calculate perimeter

The perimeter $P$ of a triangle is the sum of its three sides. For a regular triangle with side - length $s$, $P = 3s$.
Since $s = 1$, $P=3\times1 = 3$

Answer:

3