Question

Problem 16: (first taught in lesson 12) If line p bisects CT at point D and if CD = 7x - 10 and DT = 5x + 6, then find CT.

Answer 1

The pont D bisects the line CT, means that

`CD=DT`

Substitute the value in the equation to ontain the vaue of x.

`\begin{gathered} 7x-10=5x+6 \\ 7x-5x=6+10 \\ x=(16)/(2) \\ =8 \end{gathered}`

The equation for the length of line CT is,

`\begin{gathered} CT=CD+DT \\ =7x-10+5x+6 \\ =12x-4 \end{gathered}`

Substitute the value of x in the equation to obtain the value of CT.

`\begin{gathered} CT=12\cdot8-4 \\ =96-4 \\ =92 \end{gathered}`

The length of CT is 92.