Answer:
a. ZC = 13.5
b. ZA : AC = 2 : 1
Step-by-step explanation:
See the diagram of the triangle attached to the question.
a. [tex]ZA = \frac{2}{3} ZC[/tex] {Concurrency of median theorem}
⇒[tex]9 = \frac{2}{3} ZC[/tex] {Substituting the value of ZA which is given}
⇒ [tex]9 \times (\frac{3}{2}) = (\frac{3}{2}) \times \frac{2}{3} ZC[/tex] {Multiplying both sides with [tex]\frac{3}{2}[/tex]}
⇒ ZC = 13.5 {By simplification} (Answer)
b. We have [tex]ZA = \frac{2}{3} ZC[/tex] {Concurrency of median theorem}
⇒ [tex]ZA = \frac{2}{3} (ZA + AC)[/tex]
⇒ [tex]ZA = \frac{2}{3} ZA + \frac{2}{3} AC[/tex] {By distributive property of multiplication}
⇒ [tex](1 - \frac{2}{3})ZA = \frac{2}{3}AC[/tex]
⇒ [tex]\frac{1}{3} ZA = \frac{2}{3} AC[/tex]
⇒ [tex](3) \times\frac{1}{3} ZA = (3) \times\frac{2}{3} AC[/tex] {Multiplying both sides with 3}
⇒ ZA = 2 AC
⇒ ZA : AC = 2 : 1 (Answer)
