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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.

Sagot :

The pont D bisects the line CT, means that

[tex]CD=DT[/tex]

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

[tex]\begin{gathered} 7x-10=5x+6 \\ 7x-5x=6+10 \\ x=\frac{16}{2} \\ =8 \end{gathered}[/tex]

The equation for the length of line CT is,

[tex]\begin{gathered} CT=CD+DT \\ =7x-10+5x+6 \\ =12x-4 \end{gathered}[/tex]

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

[tex]\begin{gathered} CT=12\cdot8-4 \\ =96-4 \\ =92 \end{gathered}[/tex]

The length of CT is 92.

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