Step-by-step explanation:
with the height in a right triangle, we get 3 right triangles (the original one, and the 2 on both sides of the height). all 3 of these triangles are similar to each other.
that means (among other things) the ratios of 2 sides of one triangle must be the same ratio of the corresponding sides in the other triangle.
x/64 = 36/x
x² = 36×64
x = sqrt (36×64) = 6×8 = 48
long story short, x is the geometric mean value of the segments of the Hypotenuse.
geometric mean value means the nth root of the product of n numbers.
in our case - square root out of 2 numbers (the segment lengths).
