(Question 3)
Because of the definition of a perpendicular bisector, we know that angle B is a right angle (90°) an that
[tex]\bar{DB}=\bar{BE}[/tex]
Note that AB is a segment that is shared by both triangles in the image. By using SAS (Side-Angle-Side), we can find that both the triangles are congruent (they are equal). Therefore,
[tex]\begin{gathered} 3x-9=x+21\rightarrow3x-x=21+9\rightarrow2x=30 \\ \rightarrow x=\frac{30}{2} \\ \rightarrow x=15 \end{gathered}[/tex]
We know that
[tex]AE=x+21[/tex]
We'll just have to plug in the value of x we calculated to find the lenght of AE
[tex]AE=15+21\rightarrow AE=36[/tex]
Therefore, AE = 36
(Question 4)
Because of the definition of a perpendicular bisector, we know that XY splits TS right by the middle. So if TS = 10, RS would be worth half of that
Therefore, RS = 5
