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 =

Options

• 2 cm

• 4 cm

• 6 cm

• 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,

\[\angle AXY = \angle B \left( \text{Corresponding angles} \right)\]
\[\angle A = \angle A \left( \text{Common} \right)\]
\[ \therefore ∆ AXY~ ∆ ABC \left( \text{AA similarity} \right)\]

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

`(AX)/(BX)=(AY)/(YC)`

`(3x)/(1x)=(AY)/2`

`AY=(3x xx2)/(1x)`

`AY= 6cm`
Hence the correct answer is `C`