Answer:
[tex]EF = 13[/tex]
[tex]GH = 5[/tex]
[tex]EH = 13[/tex]
Step-by-step explanation:
Given
The attached figure
[tex]EG = 12[/tex]
[tex]FG = 5[/tex]
Solving (a): EF
Since m is a perpendicular bisector, then <EGF and <EGH are right-angled.
So, EF will be calculated using Pythagoras theorem which states:
[tex]EF^2 = EG^2 + FG^2[/tex]
[tex]EF^2 = 12^2 + 5^2[/tex]
[tex]EF^2 = 144 + 25[/tex]
[tex]EF^2 = 169[/tex]
Take the positive square roots of both sides
[tex]EF = \sqrt{169[/tex]
[tex]EF = 13[/tex]
Solving (b): GH
Since m is a perpendicular bisector, then GH = FG
[tex]FG = 5[/tex]
[tex]GH = FG[/tex]
[tex]GH = 5[/tex]
Solving (c): EH
Since m is a perpendicular bisector, then EH = EF
[tex]EF = 13[/tex]
[tex]EH = EF[/tex]
[tex]EH = 13[/tex]
