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. 3 < x < 9 3 ≤ x ≤ 9

Explanation:

Step1: Identify the inequality

Since the perimeter $x$ of an equilateral triangle (where all sides are equal) made from 3 equal - length pieces of a metal bar can be at most 9 feet, the inequality is $x\leq9$.

Step2: Solve the inequality

The inequality is already in its simplest form. The solution set is all real numbers $x$ such that $x$ is less than or equal to 9. In the context of the perimeter of a physical object, $x\geq0$ as well. But just considering the given inequality $x\leq9$.

Answer:

The inequality that describes the problem is $x\leq9$. The perimeter of the triangular sculpture can be at most 9 feet. So the blank should be filled with 9.