<p>in triangle ABC above, a segment is to be drawn from point B to a point P (not labeled) on side AC. if P is different form points A and C, what is one possible length of BP? The triangle is isosceles, and the equal sides are AB and BC. AB = 13. AC = 10 </p>
<p>My problem is that I have used the Pythagorean theorem to find BP and got twelve. the answer however is 12 < x < 13</p>
<p>I get how BP can be greater than twelve, but why can't it equal twelve.
This question is from and old SAT test, might be from 2004</p>
<p>If BP were to coincide with AB or CB, the length of BP would be 13, but it can’t. If BP were the altitude (which is also the median in an isosceles triangle), the length of BP would be 12. So according to the way you wrote the problem the answer could be any number between 12 and 13, INCLUDING 12, but NOT including 13. </p>
<p>So if the answer key is saying the answer can’t be 12, then either it’s a typo, or you didn’t write down a piece of information from the question (like P is not the midpoint of AC, or BP is not the median or altitude to BP).</p>
<p>Unfortunately, I’ve written it correctly. I also did consider there might be a typo in the answer key, but I thought I might have missed something so I posted it here.
Thanks for your help</p>