Find the length of the altitude drawn to a side of an equilateral triangle whose perimeter is 30.

To solve this problem, you must find the altitude, represented by a dashed line in this picture.

To do this, use the Pythagorean theorem: a^2 + b^2 = c^2

The hypotenuse (longest side in a triangle) is always the c value. So plug that into your equation for c.
This leaves you with:
a^2 + b^2 = 10^2

Next, plug in your one side length of the triangle that you have besides the hypotenuse, which is a 5. This will be your b value.
This leaves you with:
a^2 + 5^2 = 10^2

After that, square your number values to simplify the equation. To square a number, you multiply it by itself. In this case, 5 x 5 = 25 and 10 x 10 = 100.
So when you rewrite your equation you have:
a^2 + 25 = 100

To start to isolate your variable, subtract 25 on both sides of the equation to keep it balanced.
This results in:
a^2 = 75

To isolate your variable, square root the a variable and square root the other side to keep it balanced. A square root cancels out a square, so that’s how you know you can do this.

Since 75 isn’t a perfect square, find the highest perfect square that’s able to be multiplied to get 75. This is 25. 25 x 3 = 75 so put that under a radical sign.
After that, simplify the radical by taking the perfect square out of the “jail” (square root sign) this causes the perfect square to be square-rooted as it moves across to the other side of the sign. So, your final answer has a five on the outside of the radical sign with a 3 left inside.

So your final answer is:
5 radical sign 3.
(I apology for e lack of math symbols, I am on the road on vacation so I am on mobile.
I hope this still helps! :)