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 + 30 d 18x + 5 e 6(3x + 5)

Explanation:

Step1: Recall perimeter of regular hexagon

A regular hexagon has 6 equal sides. So perimeter \( P = 6\times \text{side length} \). The side length is \( 3x + 5 \).

Step2: Calculate perimeter

Using the formula, \( P=6(3x + 5) \).

Step3: Expand the expression

Expand \( 6(3x + 5) \) using distributive property \( a(b + c)=ab+ac \). So \( 6\times3x+6\times5 = 18x + 30 \).

Step4: Analyze each option

• Option A: \( 18x + 30 \) matches our expanded form.
• Option B: \( (3x + 5)(3x + 5) \) is the area - like expression (product of two sides), not perimeter.
• Option C: \( 18x + 5 \) is incorrect as we have \( 18x+30 \).
• Option D: \( 18x + 5 \) is incorrect.
• Option E: \( 6(3x + 5) \) is the factored form of the perimeter.

Answer:

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