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709 B
709 B
Question 1
\because \angle B^\prime = \angle B \quad (\text{Corresonding Line theorem}) \\
\because \angle C^\prime = \angle C \quad (\text{Corresponding Line theorem}) \\
\therefore \triangle AB^\prime C^\prime \sim \triangle ABC \quad (\text{ AA } \sim) \\ \\
\therefore \dfrac{AB^\prime}{B^\prime C^\prime} = \dfrac{AB}{BC} \\
\quad \\
\therefore \dfrac{30}{14} = \dfrac{30+x}{22} \\ \\
\quad \\
14(30+x) = 22(30) \\
\quad \\
x = \dfrac{22(30)}{14} - 30 \\
\quad \\
x = 17.1428571 \approx 17.14
\dfrac{AC^\prime}{B^\prime C^\prime} = \dfrac{AC}{BC} \\
\quad \\
\dfrac{y}{14} = \dfrac{y+15}{22} \\
\quad \\
22y = 14y + 14(15) \\
8y = 14(15) \\
y = 26.25