In the given figure, AX:XB=3:5 and XY||BC.
If XY = 18 cm, then BC = ___ .
44 cm
We are given that in the ΔABC,AX:XB=3:5 and XY||BC.
⇒XBAX=53
⇒XBAX+1=53+1
⇒XB+AXAX=5+33
⇒ABAX=83
⇒AXAB=38
Now in ΔAXYand ΔABC,
∠AXY=∠ABC (Corresponding angles)
∠XAY=∠BAC(Common in both triangles)
∴ΔAXY∼ΔABC(By AA similarity criterion)
⇒AXAB=XYBC
⇒38=18BC
∴BC=18×83 = 48 cm