SOLUTION: If line FL = 6 and line IH = 12, calculate the length of line GI. https://byuis.brainhoney.com/Resource/46824921,0/Assets/Media/Images/GEOM043_CSR1-18.jpg

Algebra ->  Trigonometry-basics -> SOLUTION: If line FL = 6 and line IH = 12, calculate the length of line GI. https://byuis.brainhoney.com/Resource/46824921,0/Assets/Media/Images/GEOM043_CSR1-18.jpg      Log On


   

Question 1042710: If line FL = 6 and line IH = 12, calculate the length of line GI.
https://byuis.brainhoney.com/Resource/46824921,0/Assets/Media/Images/GEOM043_CSR1-18.jpg
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
A theorem had been developed for this, but not remembering it, a solution may be found. Recognize the three right triangles in the figure.
Main triangle FGH
Smaller triangle FGI
Large but not main, triangle GIH
All three are right triangles.

No such named point L, but it is labeled I in your figure.
FI = 6
IH =12
Meaning that FH =18.

Use Pythagorean Theorem formula on the three right triangles.
system%28FI%5E2%2BGI%5E2=FG%5E2%2CGI%5E2%2BIH%5E2=GH%5E2%2CFG%5E2%2BGH%5E2=FH%5E2%29

Let a=GH just for convenience.
Substituting for the two other given values,
system%283%5E2%2Ba%5E2=FG%5E2%2Ca%5E2%2B12%5E2=GH%5E2%2CFG%5E2%2BGH%5E2=18%5E2%29
This has THREE unknown variables and is THREE equations.

Solve this system and finish with a formula for a=GI.

Equivalent System
system%28a%5E2-FG%5E2=-36%2Ca%5E2-GH%5E2=-144%2CFG%5E2%2BGH%5E2=324%29
and let me
skip the steps here,...
but
system%28a%5E2-FG%5E2=-36%2Ca%5E2%2BFG%5E2=180%29------easily ready for part of Elimination Method. Add corresponding members to solve for a%5E2=GI%5E2. Then just take square root.

-
I found a=sqrt%2872%29=sqrt%282%2A36%29=6sqrt%282%29.


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If you KNOW the theorem, then MathTherapy's solution is much faster.

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
If line FL = 6 and line IH = 12, calculate the length of line GI.
https://byuis.brainhoney.com/Resource/46824921,0/Assets/Media/Images/GEOM043_CSR1-18.jpg
Triangles GFI and GIH are similar

Set up the following proportion that involves GI: FI%2FGI+=+GI%2FIH, or 6%2FGI+=+GI%2F12. 

You should get: highlight_green%28GI+=+6sqrt%282%29%29

Yes, yes. It is that SIMPLE!