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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

8. Find the length of TG in the diagram below given that WG || AT, TG = x, GC = 2, CW-example-1
User Arleen
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1 Answer

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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.

User Kerissa
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