Question

1. Use the following figure for Questions (i) to (v).
Given : triangle ABC in which XY || BC
(i) AX = 3 cm and BX = 1.5 cm. Find AY : AC.
(ii) AX =3cm , XB = 5cm and AY = 6cm. Find AC.
(iii) AX = 4 cm, XB = 6 cm and AY = 3 cm. Find AC.
(iv) AX = 2x+1, XB = 2x-1, AY = 5x+5 and YC =4x+1. Find x
(v) AX = p, XB =3p+4, AY = p+3 and YC = 3p+19. Find p. ​

Answer 1

Answer 1 :

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

XY/6 = 1/4

4 XY = 6

XY = 6/4 = 3/2  

XY = 1.5 cm

Hence, the value of XY = 1.5 cm.

Answer 2 :

XY will be 3 it is the property of a triangle and AY/YC is equal to 2/3