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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
Solution
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`
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