Pergunta

Hector is building a metal sculpture in the shape of an equilateral triangle. After he divides 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? (x)/(3)leqslant 9 (x)/(3)lt 9 Solve the inequality. Then complete the sentence to describe the solution. The perimeter of the triangular sculpture can be at most square feet.
Solução

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MayraMestre · Tutor por 5 anos
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To solve this problem, we need to find the inequality that describes the situation and then solve it.<br /><br />Given information:<br />- Hector is building a metal sculpture in the shape of an equilateral triangle.<br />- Each side of the triangular sculpture can be at most 9 feet long.<br />- Let x represent the perimeter of the triangular sculpture.<br /><br />Step 1: Find the inequality that describes the problem.<br />Since each side of the triangular sculpture can be at most 9 feet long, the perimeter of the triangular sculpture can be at most 3 times 9 feet, which is 27 feet.<br /><br />Therefore, the inequality that describes the problem is:<br />$\frac{x}{3} \leq 9$<br /><br />Step 2: Solve the inequality.<br />To solve the inequality, we need to multiply both sides by 3 to isolate x:<br />$\frac{x}{3} \leq 9$<br />$x \leq 27$<br /><br />Therefore, the perimeter of the triangular sculpture can be at most 27 feet.<br /><br />The completed sentence is:<br />The perimeter of the triangular sculpture can be at most 27 feet.
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