Answer:
AY = 10 cm.
Step-by-step explanation:
Given that, ΔABC is similar to ΔAXY
and [tex]\frac{AB}{AX } = \frac{5}{3}[/tex]
⇒ [tex]\frac{AC}{AY } = [tex]\frac{BC}{XY } = \frac{5}{3}[/tex]
⇒ BC = XY× \frac{5}{3}[/tex] = \frac{20}{3}[/tex] (as XY = 4 cm given)
Now, check the attached figure,
given, BY bisects ∠XYC
let ∠XYB = ∠BYC = x
⇒ ∠AYX = 180-2x (angle on a straight line)
and also ∠AYX = ACB (similar triangle properties)
⇒ ∠ACB = 180-2x
Now, sum of angles in ΔBYC = 180°
⇒ ∠YBC = x
⇒ BC = YC (as two sides of equal angles are equal in a triangle)
⇒ YC = \frac{20}{3}[/tex]
And also [tex]\frac{AC}{AY } = \frac{5}{3}[/tex]
AC = AY + YC
⇒ [tex]\frac{AY+YC}{AY } = \frac{5}{3}[/tex]
⇒ [tex]\frac{AY+\frac{20}{3}[/tex]}{AY } = \frac{5}{3}[/tex]
⇒ 5AY = 3AY + 20
⇒ AY = 10 cm
