Question

Can anyone solve the 8th question given below??? Urgent!!

Answer 1

AY = 10 cm.

Explanation:

Given that, ΔABC is similar to ΔAXY

and
`(AB)/(AX )  = (5)/(3)`

⇒
`(AC)/(AY )  =  [tex](BC)/(XY ) = (5)/(3)`

⇒ 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
`(AC)/(AY )  = (5)/(3)`

AC = AY + YC

⇒
`(AY+YC)/(AY )  = (5)/(3)`

⇒
}{AY } = \frac{5}{3}[/tex]

⇒ 5AY = 3AY + 20

⇒ AY = 10 cm