Question

15. If in the figure, XY || BC, AX = 9 cm, XB = 7 cm, and
BC = 20 cm, then XY = [KSEEB, JUNE 2006]
A
X
(a) 11.25 cm
(b) 10.25 cm
(c) 10 cm
(d) 15 cm​

Answer 1

Step-by-step explanation:

In ∆AXY and ∆ABC ,

∠XAY = ∠BAC ( common angle )

∠AXY = ∠ABC

( corresponding angles for parallel lines XY and BC )

∠AYX = ∠ACB

( corresponding angles for parallel lines XY and BC )

Thus ,

∆AXY ~ ∆ABC ( AAA similarity )

Hence ,

AB / AX = AC / AY = BC / XY ( corresponding sides )

( 9 + 7 ) / 9 = 20 / XY

16 / 9 = 20 / XY

==> XY = ( 9 × 20 ) / 16

==> XY = 180 / 16

==> XY = 11.25 cm

Hence , Option ( a ) 11.25cm is correct .