Answer: the altitude if the equilateral triangle is 5√2
Explanation:
In an equilateral triangle, the 3 sides and the 3 angles are equal. The bisectors of each angle pass through the midpoint of the triangle. This means that each bisector divides the triangle into a two right angle triangles. The opposite side of the right angle triangle represents the altitude of the equilateral triangle. To find the altitude, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = adjacent side² + opposite side²
Opposite side = 8/2 = 4
Hypotenuse = 8
Therefore
8² = h² + 4²
h² = 64 - 14 = 50
h = √50 = √25 × √2
h = 5√2