An equilateral triangle has side of 46cm in length. how long is each altitude of the triangle (to the nearest tenth of a centimetre)?

Since it is an equilateral triangle, all sides are the same, so all amplitudes are the same.
You should use the pythagorean theorem to find the altitude.
How?:
1) Split the triangle in half. You will now have a right triangle with side C=46 and either A or B= 23.
2)Now plug these values into the equation(I chose to plug 23 in as A)
a^2 +b^2=c^2.
3) This gives you:
23^2+b^2=46^2
4) Isolate the variable and solve:
23^2+b^2=46^2
b^2=46^2-23^2
b^2=1587
5) The square root of 1587 is 39.8

The answer is 39.8 cm:)

I hope you learned something!

(^2 means squared, the ^ means the following number is the exponent, just in case ya didn't know)