Answer:
a = 4.5 units
b = 7.5 units
Step-by-step explanation:
By using mean proportional theorem in the ΔACB,
ΔACB ~ ΔADC ~ ΔCDB
[tex]\frac{AD}{CD}=\frac{CD}{DB}[/tex]
[tex]\frac{8}{6}=\frac{6}{a}[/tex]
a = [tex]\frac{6\times 6}{8}[/tex]
a = 4.5
[tex]\frac{AB}{CB}=\frac{CB}{DB}[/tex]
[tex]\frac{(a+8)}{b}=\frac{b}{a}[/tex]
Since a = 4.5
[tex]\frac{4.5+8}{b}=\frac{b}{4.5}[/tex]
b² = 4.5 × 12.5
b = √56.25
b = 7.5 units
Therefore, a = 4.5 units and b = 7.5 units will be the answer.
