question 10 of 10

what is the length of the altitude of the equilateral triangle below?

image of an equilateral triangle with side lengths $4\sqrt{3}$, split by an altitude $a$ into two $30^\circ-60^\circ-90^\circ$ triangles with base segments of length $2\sqrt{3}$

a. $\sqrt{48}$
b. 36
c. $6\sqrt{3}$
d. 2
e. $2\sqrt{3}$
f. 6

Question

question 10 of 10

what is the length of the altitude of the equilateral triangle below?

image of an equilateral triangle with side lengths $4\sqrt{3}$, split by an altitude $a$ into two $30^\circ-60^\circ-90^\circ$ triangles with base segments of length $2\sqrt{3}$

a. $\sqrt{48}$
b. 36
c. $6\sqrt{3}$
d. 2
e. $2\sqrt{3}$
f. 6

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "30-60-90 Triangle Properties", "Pythagorean Theorem" ], "new_concepts": [], "current_concepts": [ "30-60-90 Triangle Properties", "Pythagorean Theorem", "Equilateral Triangle Properties" ] } ## Identify the given values Using the *30-60-90 Triangle Properties* and *Pythagorean Theorem* knowledge points $$ \begin{aligned} &\text{Hypotenuse } (c) = 4\sqrt{3}\ &\text{Shorter leg } (b) = 2\sqrt{3}\ &\text{Altitude / Longer leg } = a \end{aligned} $$ ## Calculate the altitude length Using the *30-60-90 Triangle Properties* knowledge point $$ \begin{aligned} &a = b \cdot \sqrt{3}\ &a = 2\sqrt{3} \cdot \sqrt{3}\ &a = 2 \cdot 3 = 6 \end{aligned} $$

A. $\sqrt{48}$

B. 36

C. $6\sqrt{3}$

D. 2

E. $2\sqrt{3}$

F. 6

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Special Right Triangles" ] }

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Question

Explanation:

Identify the given values

Calculate the altitude length

Answer: