# Question 1

```math

\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 
```

```math

\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

```