2019-11-13 09:55:07 -05:00
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# Question 1
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```math
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2019-11-13 11:22:02 -05:00
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\because \angle B^\prime = \angle B \quad (\text{Corresonding Line theorem}) \\
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\because \angle C^\prime = \angle C \quad (\text{Corresponding Line theorem}) \\
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\therefore \triangle AB^\prime C^\prime \sim \triangle ABC \quad (\text{ AA } \sim) \\ \\
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\therefore \dfrac{AB^\prime}{B^\prime C^\prime} = \dfrac{AB}{BC} \\
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\quad \\
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\therefore \dfrac{30}{14} = \dfrac{30+x}{22} \\ \\
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\quad \\
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14(30+x) = 22(30) \\
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\quad \\
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x = \dfrac{22(30)}{14} - 30 \\
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\quad \\
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x = 17.1428571 \approx 17.14
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```
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```math
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\dfrac{AC^\prime}{B^\prime C^\prime} = \dfrac{AC}{BC} \\
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\quad \\
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\dfrac{y}{14} = \dfrac{y+15}{22} \\
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\quad \\
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22y = 14y + 14(15) \\
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8y = 14(15) \\
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y = 26.25
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2019-11-13 09:55:07 -05:00
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```
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