Answer:
AC ≈ 13.3 cm
Step-by-step explanation:
AC is the perpendicular bisector of DB , then
DE = EB = [tex]\frac{1}{2}[/tex] DB = [tex]\frac{1}{2}[/tex] × 12 = 6
Using Pythagoras' identity in right triangle ADE
AE² + ED² = AD²
AE² + 6² = 8²
AE² + 36 = 64 ( subtract 36 from both sides )
AE² = 28 ( take the square root of both sides )
[tex]\sqrt{AE^2}[/tex] = [tex]\sqrt{28}[/tex]
AE ≈ 5.3 cm ( to the nearest tenth )
Using Pythagoras' identity in right triangle CDE
EC² + ED² = CD²
EC² + 6² = 10²
EC² + 36 = 100 ( subtract 36 from both sides )
EC² = 64 ( take the square root of both sides )
[tex]\sqrt{EC^2}[/tex] = [tex]\sqrt{64}[/tex]
EC = 8
Then
AC = AE + EC = 5.3 + 8 = 13.3 cm
