Answer:
H = 3.46
Step-by-step explanation:
By applying mean ratio theorem in the given triangles,
[tex]\frac{BD}{AD}= \frac{AD}{DC}[/tex]
AD² = BD × DC
AD² = (6 - 4) × 4
AD = √8
AD = 2√2
By applying Pythagoras theorem in ΔABD,
Hypotenuse² = (leg 1)² + (leg 2)²
AB² = AD² + BD²
H² = (√8)² + 2²
H² = 8 + 4
H = √12
H = 3.46
