Question

geometry find the perimeter of the regular polygon. 3(x - 1) 5x - 6 the perimeter of the polygon is units.

Explanation:

Step1: Find the value of \(x\)

Since it is a regular polygon, all sides are equal. So \(3(x - 1)=5x-6\).
Expand the left - hand side: \(3x-3 = 5x-6\).
Subtract \(3x\) from both sides: \(-3=2x - 6\).
Add \(6\) to both sides: \(2x=3\), then \(x = 1.5\).

Step2: Find the length of one side

Substitute \(x = 1.5\) into \(5x-6\) (or \(3(x - 1)\)).
Using \(5x-6\): \(5\times1.5-6=7.5 - 6=1.5\).

Step3: Calculate the perimeter

A regular pentagon has \(n = 5\) sides.
The perimeter \(P=n\times\) (side length). So \(P = 5\times1.5=7.5\).

Answer:

\(7.5\)