The apothem of the triangle is equal to the height. By the Pythagorean Theorem:
s^2=h^2+(b/2)^2
s^2=h^2+b^2/4
s^2=(4h^2+b^2)/4
4s^2=4h^2+b^2, since this is an equilateral triangle s=b so
4s^2=4h^2+s^2
3s^2=4h^2
s^2=4h^2/3
s=√(4h^2/3), and the perimeter of an equilateral triangle is just 3s so
p=3√(4h^2/3)
p=√(12h^2), we were told that h=5cm so
p=√(12*25)
p=√300 cm
p=10√3 cm
p≈17.32 cm (to nearest hundredth of a centimeter)
