Question

in triangle ABC, XY //BC ,where AX=1cm ,BX=3cm and BC=6cm . Find the length of XY​

Answer 1

Answer:

SOLUTION :  

Given :  XY || BC , AX =  1 cm, XB = 3 cm, and BC = 6 cm

AB = AX + XB

AB = 1 + 3

AB = 4 cm

In ∆ AXY & ∆ABC

∠AXY = ∠ABC and ∠AYX = ∠ACB

[Corresponding angles]

∠A = ∠A

[Common]

∆ AXY ∼ ∆ABC

[By AAA similarity criterion]

ΔAXY∼ΔABC

XY/BC = AX/AB  

[Since, triangles are similar , hence corresponding sides will be proportional]

XY/6 = 1/4

4 XY = 6

XY = 6/4 = 3/2  

XY = 1.5 cm

Hence, the value of XY = 1.5 cm.

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