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Please help with this one :

A right angled triangle ABC was given in which angle C is 90 degrees. BC=4, AD=3. D is a point on BC. Given that the perimeter of triangle ABD is equal to the perimeter of triangle ADC. Then find the ratio BD/DC.

Since you posted this on PS forum, could you give the answer choices as well?

The reason why I ask is because I can get a range for the possible answer, but not an exact number.

To get the upper limit, we can use the fact that the perimeters of the two triangles are equal and since they share the side AD, we can see that AB+BD = AC + DC

and since AB has to be > AC, BD has to be < DC so BD/DC has to be < 1.

for the lower limit, since AD = 3, DC has to be < 3. and since BD + DC = 4, when DC = 3 BD = 1 and BD/DC has to be > 1/3.

Therefore, 1/3 < BD/DC < 1. This is the best I can do with the givens.

If anyone else could shine some light on this problem, I would appreciate it.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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