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schepotkina [342]
3 years ago
11

Find x. Side splitter theorem

Mathematics
1 answer:
professor190 [17]3 years ago
3 0

Answer:

x = 9

Step-by-step explanation:

The outer and inner triangles are similar, thus the ratios of corresponding sides are equal, that is

\frac{8}{8+4} = \frac{x-3}{x} , that is

\frac{8}{12} = \frac{x-3}{x} ( cross- multiply )

12(x - 3) = 8x

12x - 36 = 8x ( subtract 8x from both sides )

4x - 36 = 0 ( add 36 to both sides )

4x = 36 ( divide both sides by 4 )

x = 9

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See explanation

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<u><em>1st photo:</em></u>

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<u><em>2nd photo:</em></u>

(a) GEH ~ FGH ~ FEG

<em>similar triangles, use similar corners in the right order</em>

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<em />

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<em />

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