Answer:
a = 9.849
b = 20.25
c = 491.03
Step-by-step explanation:
By using Pythagoras theorem in the right triangle BDC,
(Hypotenuse)² = (Leg 1)² + (Leg 2)²
BC² = BD² + DC²
a² = 9² + 4²
a = [tex]\sqrt{(81+16)}[/tex]
a = [tex]\sqrt{97}[/tex]
a = 9.8489
a ≈ 9.849 units
By mean proportional theorem,
[tex]\frac{\text{DC}}{\text{BD}}=\frac{\text{BD}}{\text{AD}}[/tex]
AD × DC = BD²
b × 4 = 9²
b = [tex]\frac{81}{4}[/tex]
b = 20.25 units
BY Pythagoras theorem in ΔADB,
AB² = AD² + BD²
c² = b² + 9²
c² = (20.25)² + 9²
c² = 410.0625 + 81
c = 491.0625
c = 491. 063 units
