In the following figure, AF is the perpendicular-bisector of BD, AD = 15, and DF = 13. Find AB + BF
since AF is the perpendicular bisector of BD, therefore BF=FD. since DF=FD=13, BF=13
now, if you draw this figure, you will see that you form a right triangle (AFD) when you connect A and D,, connecting A and B, you form another right triangle,,
since they share a common height, and BF=FD, it follows that AD=AB=15
therefore,
13 + 15 = 28
hope this helps~ :)
To find AB + BF, we need to determine the lengths of AB and BF.
Since AF is the perpendicular-bisector of BD, it means that AF divides BD into two equal parts, AB and BF.
First, let's find the length of AB.
Since AF is the perpendicular bisector of BD, we can conclude that angle AFD is a right angle. Therefore, we can use the Pythagorean theorem to find the length of AB.
Using the Pythagorean theorem, we have:
AF^2 = AD^2 - DF^2 (since AF is the hypotenuse, AD is one of the legs, and DF is the other leg)
Substituting the given values, we get:
AF^2 = 15^2 - 13^2
AF^2 = 225 - 169
AF^2 = 56
Taking the square root of both sides, we get:
AF = √56
AF ≈ 7.48
Since AF is the perpendicular bisector of BD, AB and BF are equal in length.
Therefore, AB ≈ BF ≈ 7.48.
Finally, to find AB + BF, we add their lengths:
AB + BF ≈ 7.48 + 7.48
AB + BF ≈ 14.96
So, AB + BF is approximately 14.96.