Question

Look at the figure below.

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_0300_Subtest_05_20/image0014e1c8e45.jpg

A right triangle PQR with right angle at R is drawn. The length of the base PQ is 12. The length of the leg QR is 10. The altitude RS is drawn that meets PQ at S. The length of SQ is x.

What is the value of x rounded to the nearest tenth?

1.7

8.3

14.4

11.0

Answer 1

\[\frac{x}{10} = \frac{10}{12}\]Can you solve this?

Answer 2

100= 12x
8.3333333333333333333333333333333 = x

Answer 3

Yup :)

Answer 4

I just don't understand which numbers to pick.

Answer 5

Alright. Here's a rule I learned.

Answer 6

There are three possible geometric means you can use.

Answer 7

Where the two lines meet is the geometric mean and the two segments that are intersected are the extremes or other numbers.

Answer 8

This is the A in a strategy called ALL

Answer 9

I still don't understand :\

Answer 10

Alright. Let's say we have the following.

Using what I said above, you would do \[\frac{25}{x} = \frac{x}{16}\]Do you see?

Answer 11

So for the one in the middle, you put on bottom then one number from a triangle. Then you put X on top now and then the other number on the bottom? Basically so that the X's cross multiply each other and the numbers cross multiply on themselves?

Answer 12

Yes.

Answer 13

Okay, thankyou so much(:

Answer 14

There are 2 more ways that geometric means work using this. Do you want to know?

Answer 15

Yes please

Answer 16

Alright. There are 2 more geometric means.

Here are the two proportions here.
\[\frac{3}{x} = \frac{x}{7}\]\[\frac{4}{y} = \frac{y}{7}\]