Question

If the altitude of an equilateral triangle is 9 what is the perimeter

Answer 1

$\text{Altitude formula=} \dfrac{s \sqrt{3} }{2} \\ \\ 9= \dfrac{s \sqrt{3} }{2} \\ \\ s \sqrt{3}=18 \\ \\ s= \dfrac{18}{ \sqrt{3} } \\ \\ s = \dfrac{18 \sqrt{3} }{3} \\ \\ s =6\sqrt{3} \\ \\ \\ P = 3s \\ \\ P=3 \times 6 \sqrt{3} \\ \\ P = 18 \sqrt{3} \\ \\ \\ P \approx 3 \times 6 \times 1.73 \\ \\ P \approx 31,14$

Answer 2

The angles in an equilateral triangle  are 60 degrees.

sin 60 = 9 / h     where h is  hypotenuse ( = side of the triangle)

h = 9 / sin 60 = 10.392

Perimeter = 3 * h = 31.18  to nearest hundredth