How to find the perimeter of an equilateral triangle if its height is 25?

Let the side of our equilateral triangle be equal to the variable a.

Then half of the side of our equilateral triangle can be represented through a / 2.

Since we know from the condition of the task that the height in such a triangle is 25, then it is possible to write the equation using the corresponding formula from the Pythagorean theorem and determine the length of the side:

a ^ 2 – (a / 2) ^ 2 = 252;

3/4 * a ^ 2 = 625;

a ^ 2 = 833, (3).

a1 = √833, (3);

a2 = -√833, (3) (not suitable).

Then the perimeter is:

3 * √833, (3) = 3√833, (3).

Answer: 3√833, (3).