Question

the side length of an equilateral triangle is 6 cm. what is the height of the triangle?
\\( \frac { 3 } { \sqrt { 3 } } \\) cm
\\( \frac { 6 } { \sqrt { 3 } } \\) cm
\\( 3 \sqrt { 3 } \\) cm
\\( 6 \sqrt { 3 } \\) cm

Explanation:

Step1: Divide the equilateral triangle

Divide the equilateral triangle into two right - angled triangles. The hypotenuse of each right - angled triangle is the side of the equilateral triangle (\(a = 6\) cm), and the base of each right - angled triangle is \(\frac{a}{2}=\frac{6}{2}=3\) cm.

Step2: Apply the Pythagorean theorem

Let the height of the equilateral triangle be \(h\). According to the Pythagorean theorem \(a^{2}=b^{2}+h^{2}\) (where \(a\) is the hypotenuse and \(b\) is the base of the right - angled triangle). Substitute \(a = 6\) and \(b = 3\) into the formula:

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Answer:

C. \(3\sqrt{3}\text{ cm}\)