[tex] \\
\text{Two Triangles are said to be similar if the ratios of their corresponding sides are equal}\\
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\text{In the given diagram, the larger triangle has sides 6+8=}14 \ and \ 3x\\
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\text{and the smaller triangle has sides }(2x-2) \ and \ 8\\
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\text{The ratios can be written as follows}\\
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\frac{3x}{2x-2}= \frac{14}{8}\\
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\text{Simplify, we get}\\
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8*3x=14(2x-2)\\
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24x=28x-28\\
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\text{Take like terms together and simplify we get}\\
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28x-24x=28\\
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4x=28\\
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x=7\\ [/tex]
