Perimeter and Area

The perimeter of a triangle is the sum of the lengths of the three sides.

EXAMPLE 6: To find the perimeter of an equilateral triangle whose height is 12, note that the height divides the triangle into two 30-60-90 right triangles. In the figure below, use KEY FACT H8:

$AD=\frac{12}{\sqrt{3}}\mathrm{and}s=\text{2}\left(\frac{12}{\sqrt{3}}\right)$

$s=2\left(\frac{12}{\sqrt{3}}\right)=\frac{24}{\sqrt{3}}=\frac{24}{\sqrt{3}}\mathbf{·}\frac{\sqrt{3}}{\sqrt{3}}=\frac{24\sqrt{3}}{3}=8\sqrt{3}$

So, the perimeter is $3s=24\sqrt{3}$.

Key Fact H9