Question

which set of values could be the side lengths of a 30-60-90 triangle?

a. \\(\\{6, 12, 12\sqrt{2}\\}\\)
b. \\(\\{6, 12, 12\sqrt{3}\\}\\)
c. \\(\\{6, 6\sqrt{2}, 12\\}\\)
d. \\(\\{6, 6\sqrt{3}, 12\\}\\)

Explanation:

Recall the ratio of side lengths

Using the 30-60-90 Triangle Properties knowledge point

$$ x : x\sqrt{3} : 2x $$

Identify the shortest side

Using the 30-60-90 Triangle Properties knowledge point

$$ x = 6 $$

Calculate the remaining side lengths

Using the 30-60-90 Triangle Properties knowledge point

$$
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$$

Match with the given options

Using the 30-60-90 Triangle Properties knowledge point

$$ \{6, 6\sqrt{3}, 12\} $$

Answer:

• A. \(\{6, 12, 12\sqrt{2}\}\)
• B. \(\{6, 12, 12\sqrt{3}\}\)
• C. \(\{6, 6\sqrt{2}, 12\}\)
• D. \(\{6, 6\sqrt{3}, 12\}\) (Correct answer)