Sunday, 4 January 2015

geometry - Why does the Pythagorean Theorem not work on this problem in the way that I used it?

To begin with, I apologize for the vagueness of my question. It's hard to explain what exactly my question entails without seeing what process I went through to try to solve the problem. My question is just that I don't understand why my method did not work.



The problem: In Figure 8, P is a point in the square of side-length 10 such that it is equally distant from two consecutive vertices and from the opposite side AD. What is the length of BP?
A) 5 B) 5.25 C) 5.78 D) 6.25 E)7.07



(I apologize for the crude drawing, the problem was in my book so I had to improvise using Paint)
Figure 8



What I did: Since BC and CD are both 10, I used the pythagorean theorem to get the length of diagonal BD (sqrt 200) and divided by 2. My answer was therefore E) 7.07.




What my book did: Set BP to x, and the length of (B and midpoint of AB) to 10-x. To complete the triangle, they set the length of (P and midpoint of AB) to 5. Then they used the Pythagorean Theorem to do x^2 = (10-x)^2 + 5^2, yielding an answer of D) 6.25.



While I understand how they did it, I simply cannot understand why my method didn't work. Is there some law that I'm not aware of pertaining to this problem? Since my incorrect answer was an answer choice, I assume there is a common error I'm making that was set as a trap.



Could someone explain this to me? Thank you very much.

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