Question 13 Marks

In the following figure, XY || seg AC. If $2AX=3BX$ and $XY=9$. Complete the activity to find the value of AC.

Activity :
$2AX=3BX$ (Given)
$\therefore \frac{AX}{BX} = \frac{3}{⬜}$
$\frac{AX+BX}{BX} = \frac{3+2}{2}$ .......... (by componendo)
$\frac{⬜}{BX} = \frac{5}{2}$ .......... (I)
Now $\Delta BCA \sim \Delta BYX$ .......... ($⬜$ test of similarity)
$\therefore$ $\frac{BA}{BX} = \frac{AC}{XY}$ .......... (corresponding sides of similar triangles)
$\frac{⬜}{⬜} = \frac{AC}{9}$ .......... (from I)
$\therefore$ $AC =⬜$

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