Question

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

Activity:

2AX = 3BX

∴ `"AX"/"BX" = 3/2`

∴ `(AX + BX)/"BX"` = `(square + square)/2`     ...[By componendo]

∴ `"AX"/"BX" = square/2`

ΔBCA ~ ΔBYX     ...[`square` test of similarity]

∴ `"BA"/"BX" = "AC"/"XY"`     ....[corresponding sides of similar triangles]

∴ `5/square = "AC"/9`

∴ AC = `square`

Answer 1

2AX = 3BX

∴ `"AX"/"BX" = 3/2`

∴ `(AX + BX)/"BX"` = \[\frac{\boxed{3} + \boxed{2}}{2}\]    ...[By componendo]

∴ `"AB"/"BX"` = \[\frac{\boxed5}{{2}}\]

Δ BCA ~ Δ BYX     ...[\[\boxed{AA}\] test of similarity]

∴ `"BA"/"BX" = "AC"/"XY"`     ....[corresponding sides of similar triangles]

∴ \[\frac{5}{\boxed{2}}\] = `"AC"/9`

∴ AC = `45/2`

∴ AC = \[\boxed{22.5}\]