Similar Triangles

[twilight-er000]

The two triangles ain the following figure are similar. Find the value of x to the nearest thousandth.

[url="http://s378.photobucket.com/albums/oo228/headoverheelsxx3/?action=view&current=untitled2.jpg"][img]http://i378.photobucket.com/albums/oo228/headoverheelsxx3/untitled2.jpg[/img][/url]

http://s378.photobucket.com/albums/oo22 ... itled2.jpg
^^^url for the figure

 

[Loren]

I see three triangles. Are they all similar? Are they all right triangles? Answer those questions and you may see how to solve your problem. If not, show us your work, and/or let us know your thinking.

 

[twilight-er000]

only the two small triangles are similar to each other. I found the value of 12 with the pythagoream theorem but now I am lost as to how to find X. The middle line is perpendicular so the two small triangles are right triangles.

 

[Denis]

IF they're similar, then they're identical, since they share the side = 12. So x = 20.

 

[Mrspi]

You said the two smaller triangles are similar...but we need to know the NAMES of the triangles so we can see how the corresponding parts match up.

If 12 is the "longer leg" in the small, left-hand triangle, you'd have this relationship:

hypot/longer leg = hypot/longer leg

x /12 = 20/16

That will give you a different answer than the one Denis gave you.

Without more information, we can't tell which is right.

 

[Loren]

I think you will find that all three triangles are similar. You need to understand why.

 

[matt000r000]

purely based on the picture, i would say mrspi has the correct value, but he is right, there is not enough information to tell. also, loren is right too. there are three right triangles. the first with sides including 20, 16, and 12. the seccond including sides x and 12. the third including sides x and 20. this is a very special figure if thats the case, and it is home to many unique ratios and poportions, in the end giving the pythagorean theorem. if this is what you're studying or about to study, i would highly recommend solving this problem yourself.

 

[stapel]

purely based on the picture, i would say mrspi has the correct value, but he is right...

I made the same mistake earlier.

It's "Mrs. Pi", not "Mr. Spi". :lol: