Question

a regular hexagon has side length 3x + 5. select all of the expressions that show the perimeter of the hexagon. a 18x + 30 b (3x + 5)(3x + 5) c 15x + 25 d 18x + 5 e 6(3x + 5)

Explanation:

Step1: Recall perimeter formula for regular hexagon

A regular hexagon has 6 equal - length sides. If the side - length of a regular hexagon is \(s\), the perimeter \(P = 6s\). Here, \(s=3x + 5\), so \(P = 6(3x + 5)\).

Step2: Expand the expression

Using the distributive property \(a(b + c)=ab+ac\), where \(a = 6\), \(b = 3x\), and \(c = 5\). We get \(6\times3x+6\times5=18x + 30\).

Answer:

A. \(18x + 30\), E. \(6(3x + 5)\)