Question

Pm is the perpendicular bisector of ab am =and 12 the perimeter of pab is 52 find length of bp

Answer 1

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:

`BP\text{ = }(28)/(2)=14`

so that, we can conclude that the correct answer is:

`BP=\text{ 14}`