Q.3 (A)(1) In the following figure, XY || seg AC. If 2AX = 3BX and XY = 9. Complete the activity to find the value of AC.[Figure: Δ ABC with X on side AB and Y on side BC, XY parallel to AC.]Activity :2AX = 3BX (Given)∴ \(\dfrac{AX}{BX} = \dfrac{3}{\…

Q.3 (A)(1) In the following figure, XY || seg AC. If 2AX = 3BX and XY = 9. Complete the activity to find the value of AC.

[Figure: Δ ABC with X on side AB and Y on side BC, XY parallel to AC.]

Activity :

2AX = 3BX (Given)
∴ \(\dfrac{AX}{BX} = \dfrac{3}{\text{____}}\)
\(\dfrac{AX + BX}{BX} = \dfrac{3 + 2}{2}\) .......... (by componendo)
\(\dfrac{\text{____}}{BX} = \dfrac{5}{2}\) ................ (I)
Now Δ BCA ~ Δ BYX ............. (____ test of similarity)
∴ \(\dfrac{BA}{BX} = \dfrac{AC}{XY}\) .............. (corresponding sides of similar triangles)
∴ \(\dfrac{\text{____}}{\text{____}} = \dfrac{AC}{9}\) .............. from (I)
∴ AC = ____