Triangle

Question

In the attached figure, AB=10, CD=40, Find EF?

gmat1220 · Answer

I think we need the sides BF and BC.

maheshsrini · Answer

The points F & C are the adjacent points to B in the same line.

fluke · Answer

This is not a complete question. 
1. Is AB||CD||EF?
2. Are AEC and BED straight lines.

Even with above information, we will need something else to deduce the length of EF.

What is the source of the question?

ravsg · Answer

yeah we need BF, FC or the ratio

Warlock007 · Answer

Dear Fluke considering AC & DB straight Lines i got the answer EF = 8 by property of similar triangles Explaination let BF = x & FC = z & EF = y (which we need to find out) from similar triangle properties 40/y=x+z/x ..........(1) 10/y=x+z/z............(2) now with both the equation we have 40x=10z so x/z=1/4 now with componendo rule of ratios we have x+z/z=(1+4)/4= 5/4 now putting this back in eqn (2) we get y = 8

please let me know the OA

fluke · Answer

Correct. Good job.

Warlock007 · Answer

Thank God It was correct...... :-D

thanks for the kudos as well fluke :-D

KarishmaB · Answer

Good call Warlock007. In my geometry class, I like to discuss a few common figures in which the concept of similar triangles jumps right out at you. Giving below some of them. Ques2.jpg See if you can figure out the similar triangles and the reason they are similar in each one of these cases. (Angles that look 90 are 90 here). Most of them have right triangles/lines parallel to a side of the triangle.

Warlock007 · Answer

Hey thanks karishma i deserve a kudos from you then.......... :-D

thanks for the figures

noboru · Answer

10/BC=EF/FC
40/BC=EF/BF

Solving, I got EF=8.

maverick04 · Answer

I got 8 using the similar triangles concept..

puneetj · Answer

good explanation Warlock007 and thanks for the diagrams Karishma...(need to attend your veritas class

Warlock007 · Answer

Hey Puneet what are you waiting for man give me kudos.......... :beer

sudhir18n · Answer

from similar triangle properties
40/y=x+z/x ..........(1)
10/y=x+z/z............(2)

How do we get this equation? which property of similar triangle is this?

Warlock007 · Answer

this is about the ratios of the sides refer to what karishma has explained in her previous post or refer to bunuel or to OG theory even that will help you to understand this better hope this helps

puneetj · Answer

Ok Warlock............but don't forget to give it back someday :-D

Warlock007 · Answer

Sure man i never get stingy when it comes for kudos.... :cool

amit2k9 · Answer

using similar triangle 
EF/AB = CF/BC
EF/CD = BF/BC

4EF = 40-EF thus EF = 8

Triangle

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