Answer:
x = 5√3
Explanation:
We will use the Pythagorean theorem with a and b as the lengths of the legs, and c as the length of the hypotenuse.
a² + b² = c²
We need two of the three lengths of a, b, and c, so we can find the third length.
The height divides the equilateral triangle into two right triangles.
Look at one of the right triangles.
One leg is half the side of the triangle.
a = 10/2 = 5
One leg is the height.
b = x
The hypotenuse is the side of the equilateral triangle.
c = 10
a² + b² = c²
5² + x² = 10²
25 + x² = 100
x² = 75
x = √75
x = 5√3