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