Question

In ΔABC, seg XY || side AC. If 2AX = 3BX and XY = 9, then find the value of AC.

Answer 1

Given, 2AX = 3BX

∴ `("AX")/("BX") = 3/2`

`("AX" + "BX")/("BX") = (3 + 2)/2` ......[By componendo]

∴ `("BA")/("BX") = 5/2`  [A – X – B]  ......(i)

In ΔBCA and ΔBYX,

`{:(∠"BCA" ≅ ∠"BYX"),(∠"BAC" ≅ ∠"BXY"):}}`  ......[Corresponding angles]

∴ ΔBCA ∼ ΔBYX   ......[By AA test of similarity]

∴ `("BA")/("BX") = ("AC")/("XY")`  ......[Corresponding sides of similar triangle]

∴ `5/2 = ("AC")/9`

∴ AC = `(5 xx 9)/2 = 45/2`

∴ AC = 22.5 units