Question 936442
a) Geometric mean is the nth root of the product of n numbers.
b) Consider a right triangle ABC with angle c = 90 degrees.  Drop an altitude(a) from angle c to point D on line segment AC.  Now we have two right triangles that are similar, ABD and DBC.  Also, we choose AD = 4 and DC = 11 and AC is the hypotenuse of ABC.  Since the triangles are similar, we have the following relationship involving the two triangles.
4/a = a/11
a^2 = 44
a = 2*square root(11)
note that a is the geometric mean of AD(4) and DC(11), that is
a = square root(44) = 2*square root(11)