SOLUTION: What is a geometric mean? Explain the different triangle and similarity relationships of the geometric mean. I know that Geometric Mean is a special average where I would multip

Question 936442: What is a geometric mean? Explain the different triangle and similarity relationships of the geometric mean.
I know that Geometric Mean is a special average where I would multiply numbers together then take their square root (if only two numbers), cube root (if three numbers) and so forth and so on. (But I'm having trouble answering the second part of the question please help.)
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
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)

RELATED QUESTIONS
Explain the different triangle and similarity relationships of the Geometric... (answered by Theo)

What is the geometric mean of: a and 4a? What is the geometric mean of: 2a and... (answered by stanbon)

what is the geometric mean of 10 and... (answered by Theo)

Twelve is the geometric mean of 9 and what number? (answered by JBarnum)

what is the geometric mean of 8 and... (answered by jim_thompson5910)

what is the geometric mean of 2a and 4a (answered by MathLover1)

What is the geometric mean of 9 and... (answered by ben720)

What is the geometric mean of 2 and 25? (answered by Theo)