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Description:

The geometric mean of two numbers is the square root of the product. Using proportions, you can set up ratios, cross multiply, and then simplify to get the answer. Easy as pie.

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Transcript

00:05

Geometric Mean, a la Shmoop.

00:13

A triangle at the bar, named Aybeesee, or ABC for short, wants you to guess her height.

00:20

She's a supermodel... being a triangle, she's in really great... shape...

00:24

...so she's really proud of her height.

00:27

Her height is the length from point A, where her 90° angle is, to her hypotenuse at point D.

00:35

This line, called the altitude, splits her into two smaller right triangles.

00:40

Knowing that, there's a possibility that Aybeesee is really two baby triangles in a cocktail dress.

00:47

She gives you a hint....the length from C to D is 9 feet, and the length from D to B is 4.

00:55

What is her height?

00:57

If we want to find Aybeesee's height, we can use something called the geometric mean.

01:06

It's not as cruel as it sounds.

01:08

The geometric mean of two numbers is the square root of the product.

01:13

Sounds simple, but how do we use it?

01:16

First, let's take what we know.

01:18

We can use the similarity of the two triangles and make a proportion out of the sides.

01:26

The proportions tell us that CD over AD equals AD over BD.

01:33

Plugging in these lengths, we get that 9 over x equals x over 4.

01:38

Cross multiplying gives us: x squared equals 9 times 4

01:45

Take the square root of both sides, and we get x equals plus or minus the square root of 9 times 4.

01:52

And look the square root of two numbers multiplied together...is the geometric mean.

02:00

Since Aybeesee can't have a negative height,

02:03

we take the positive answer only... ...so her height is 6 feet.

02:09

Who knows?

02:10

Maybe she'll swoon at your knowledge of geometric means and pay for your Coca-Cola.

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