Question

XY is drawn parallel to the base BC of a ∆ABC cutting AB at X and AC at Y. If AB = 4 BX and YC = 2 cm, then AY =

(a) 2 cm
(b) 4 cm
(c) 6 cm
(d) 8 cm

Answer 1

Given: XY is drawn parallel to the base BC of a ΔABC cutting AB at X and AC at Y. AB = 4BX and YC = 2 cm.

To find: AY

In ΔAXY and ΔABC,

$$\begin{gathered} \angle \mathrm{AXY}=\angle \mathrm{B}\left(\mathrm{Corresponding}\mathrm{angles}\right) \\ \angle \mathrm{A}=\angle \mathrm{A}\left(\mathrm{Common}\right) \\ \therefore ∆\mathrm{AXY}~∆\mathrm{ABC}\left(\mathrm{AA}\mathrm{similarity}\right) \end{gathered}$$

We know that if two triangles are similar, then their sides are proportional.

It is given that AB = 4BX.

Let AB = 4x and BX = x.

Then, AX = 3x

Hence the correct answer is .