+0

# What is the ratio of the measure of a regular hexagon's longest diagonal to the measure of its perimeter? Express your answer as a common fr

0
48
2

What is the ratio of the measure of a regular hexagon's longest diagonal to the measure of its perimeter? Express your answer as a common fraction.

Feb 16, 2023

#1
0

Feb 17, 2023
#2
+2602
+1

Split the hexagon into 6 equilateral triangles, and let the sides of the hexagon be s.

The longest diagonal would be the one between two opposite vertices, which is comprised of the sides of 2 equilateral triangles with side length s, so its length is 2s.

The perimeter of the hexagon is 6 times the side of the hexagon or 6s.

So, the ratio is $${2s \over 6s} = {\color{brown}\boxed{1 \over 3}}$$

Feb 17, 2023