Question

triangle mno is an equilateral triangle with sides measuring $16\sqrt{3}$ units.
what is the height of the triangle?
12 units
24 units
36 units
72 units

Explanation:

Step1: Find the length of \(MR\)

In an equilateral triangle, the height \(NR\) bisects the base \(MO\). So \(MR=\frac{1}{2}MO\). Given \(MO = 16\sqrt{3}\), then \(MR=\frac{1}{2}\times16\sqrt{3}=8\sqrt{3}\).

Step2: Apply the Pythagorean theorem in \(\triangle MNR\)

In right - triangle \(MNR\), by the Pythagorean theorem \(NR^{2}+MR^{2}=MN^{2}\). Let \(NR = h\), \(MN = 16\sqrt{3}\) and \(MR = 8\sqrt{3}\). Then \(h^{2}+(8\sqrt{3})^{2}=(16\sqrt{3})^{2}\).

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Answer:

24 units