Question

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Answer 1

a. ZC = 13.5

b. ZA : AC = 2 : 1

Explanation:

See the diagram of the triangle attached to the question.

a.
`ZA = (2)/(3) ZC` {Concurrency of median theorem}

⇒
`9 = (2)/(3) ZC` {Substituting the value of ZA which is given}

⇒
`9 * ((3)/(2)) = ((3)/(2)) * (2)/(3) ZC` {Multiplying both sides with
`(3)/(2)`}

⇒ ZC = 13.5 {By simplification} (Answer)

b. We have
`ZA = (2)/(3) ZC` {Concurrency of median theorem}

⇒
`ZA = (2)/(3) (ZA + AC)`

⇒
`ZA = (2)/(3) ZA + (2)/(3) AC` {By distributive property of multiplication}

⇒
`(1 - (2)/(3))ZA = (2)/(3)AC`

⇒
`(1)/(3) ZA = (2)/(3) AC`

⇒
`(3) *(1)/(3) ZA = (3) *(2)/(3) AC` {Multiplying both sides with 3}

⇒ ZA = 2 AC

⇒ ZA : AC = 2 : 1 (Answer)