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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 - Mathematics

MCQ

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

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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`

Concept: Triangles Examples and Solutions
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 7 Triangles
Q 7 | Page 132
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