Question

Hector is building a metal sculpture in the shape of an equilateral triangle. After he divides a metal bar into 3 equal pieces, Hector figures each side of the triangular sculpture can be at most 9 feet long.
Let x represent the perimeter of the triangular sculpture. Which inequality describes the problem?
Solve the inequality. Then, complete the sentence to describe the solution.
The perimeter of the triangular sculpture can be at most feet.

Answer 1

Let each side of the equilateral triangle be represented by \( s \). Since there are 3 equal sides in an equilateral triangle, the perimeter \( x \) can be expressed as:

\[
x = 3s
\]

According to the problem, each side can be at most 9 feet long, so we can set up the inequality:

\[
s \leq 9
\]

Now, substituting this inequality into the perimeter expression:

\[
x = 3s \implies x \leq 3 \times 9
\]

Calculating the right-hand side gives:

\[
x \leq 27
\]

Thus, the inequality that describes the problem is:

\[
x \leq 27
\]

### Conclusion:
The perimeter of the triangular sculpture can be at most **27** feet.