Question:
Solution:
we know that the perimeter of the given triangle is 52, thus, we get the following equation:
AM + MB + AP+BP = 52 EQUATION 1
Now, notice that 12=AM = MB
then MB=12
now, remember that the Perpendicular Bisector Theorem states that a point is on the perpendicular bisector of a segment if and only if it is equidistant from the endpoints of the segment. By the converse of this theorem, this means that:
AP = BP.
Then, equation 1, es equivalent to:
2(AM) + 2(BP)=52
this is equivalent to
24 + 2(BP)=52
this is equivalent to:
2(BP)= 52-24 = 28
now, solving for BP, we get:
[tex]BP\text{ = }\frac{28}{2}=14[/tex]so that, we can conclude that the correct answer is:
[tex]BP=\text{ 14}[/tex]
