Question

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 of Regular Hexagon

A regular hexagon has 6 equal sides. If each side length is \( 3x + 5 \), then the perimeter \( P \) is the sum of all 6 sides, so \( P=6\times(3x + 5) \).

Step2: Simplify the Perimeter Expression

Simplify \( 6\times(3x + 5) \):
Using the distributive property \( a(b + c)=ab+ac \), we get \( 6\times3x+6\times5 = 18x + 30 \).

Step3: Analyze Each Option

• Option A: \( 18x + 30 \) matches the simplified perimeter expression.
• Option B: \( (3x + 5)(3x + 5)=(3x + 5)^2 \) is the area of a square with side \( 3x + 5 \), not a perimeter, so B is incorrect.
• Option C: \( 15x + 25 \) does not match \( 18x + 30 \), so C is incorrect.
• Option D: \( 18x + 5 \) does not match \( 18x + 30 \), so D is incorrect.
• Option E: \( 6(3x + 5) \) is the unsimplified form of the perimeter (since perimeter of regular hexagon is 6 times side length), so E is correct.

Answer:

A, E