Question

In the following figure, XY is parallel to BC, AX = 9 cm, XB = 4.5 cm and BC = 18 cm.

Find :

1. `(AY)/(YC)`
2. `(YC)/(AC)`
3. XY

Answer 1

i. Given that XY || BC

So, ΔAXY ∼ ΔABC

`=> (AY)/(YC) = 9/4.5`

`=> (AY)/(YC) = 2/1`

`=> (AY)/(YC) = 2`

ii. Given that XY || BC

So, ΔAXY ∼ ΔABC

`=> (AX)/(AB) = (AY)/(AC)`

`=> (AY)/(AC) = 1/(2 + 1)`

`=> (YC)/(AC) = 1/3`

iii. In ΔAXY and ΔABC,

∠XAY = ∠BAC  ...(Common angle)

∠AXY = ∠ABC   ...(Corresponding angles for parallel lines, XY || BC)

∠AYX = ∠ACB    ...(Corresponding angles for parallel lines, XY || BC)

Thus, ΔAXY ∼ ΔABC

Hence, `(AX)/(AB) = (XY)/(BC)`  ...(Using similar triangle property)

`(AX)/(AX + XB) = (XY)/18`

`9/(9 + 4.5) = (XY)/18`

`XY = (18 xx 9)/(13.5)`

XY = 12 cm