Question

question 9 of 10 what is the length of the altitude of the equilateral triangle below? a. 6 b. 2 c. 2√3 d. 6√3 e. √48 f. 36

Explanation:

Step1: Identify right triangle sides

Hypotenuse = \(4\sqrt{3}\), shorter leg = \(2\sqrt{3}\)

Step2: Apply Pythagorean theorem

\(a^2 + (2\sqrt{3})^2 = (4\sqrt{3})^2\)

Step3: Calculate squares

\(a^2 + 12 = 48\)

Step4: Solve for \(a^2\)

\(a^2 = 48 - 12 = 36\)

Step5: Find \(a\)

\(a = \sqrt{36} = 6\)

Answer:

A. 6