Question

8. Find the length of TG in the diagram below given that WG || AT, TG = x, GC = 2, CW = x + 5 and WA = 12. W А

Answer 1

The next proportion must be satisfied

`(CW)/(WA)=(CG)/(GT)`

Replacing with data,

`\begin{gathered} (x+5)/(12)=(2)/(x) \\ (x+5)\cdot x=2\cdot12 \\ x^2+5x=24 \\ x^2+5x-24=0 \end{gathered}`

Using quadratic formula,

`\begin{gathered} x_(1,2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_(1,2)=\frac{-5\pm\sqrt[]{5^2-4\cdot1\cdot(-24)}}{2\cdot1} \\ x_(1,2)=\frac{-5\pm\sqrt[]{25^{}+96}}{2} \\ x_(1,2)=\frac{-5\pm\sqrt[]{121}}{2} \\ x_1=(-5+11)/(2)=3 \\ x_2=(-5-11)/(2)=-8 \end{gathered}`

The negative answer has no sense in this problem, then the length of TG is 3.