Question

the height of an equilateral triangle is (4sqrt{3}). what is the perimeter of the equilateral triangle?
12 units
(12sqrt{3}) units
24 units
(24sqrt{3}) units

Explanation:

Step1: Use the height formula for an equilateral triangle

The height \(h\) of an equilateral triangle with side length \(a\) is \(h = \frac{\sqrt{3}}{2}a\). Given \(h = 4\sqrt{3}\), we set up the equation \(\frac{\sqrt{3}}{2}a=4\sqrt{3}\).

Step2: Solve for the side length \(a\)

Divide both sides of the equation \(\frac{\sqrt{3}}{2}a = 4\sqrt{3}\) by \(\sqrt{3}\): \(\frac{1}{2}a = 4\). Then multiply both sides by \(2\) to get \(a = 8\).

Step3: Calculate the perimeter \(P\)

The perimeter \(P\) of an equilateral triangle is \(P = 3a\). Substitute \(a = 8\) into the formula: \(P=3\times8 = 24\).

Answer:

24 units