Question

1. geometry the sides of the hexagon shown are equal in length. the perimeter of the hexagon is at most 42 inches. find the possible side lengths of the hexagon.

Explanation:

Step1: Define variable for side length

Let $s$ = side length (in inches).

Step2: Set up perimeter inequality

A hexagon has 6 equal sides, so perimeter $P=6s$. The perimeter is at most 42, so:
$$6s \leq 42$$

Step3: Solve for $s$

Divide both sides by 6:
$$s \leq \frac{42}{6}$$
$$s \leq 7$$
Since side length must be positive: $s > 0$

Answer:

The possible side lengths are all positive real numbers less than or equal to 7 inches, or $0 < s \leq 7$ inches.