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.