$XY is drawn parallel to the base BC of a Δ A B C cutting AB at X and AC at Y. If AB = 4 cm, BX and YC = 2 cm,$
$then find the measure of AY .$

2 cm

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4 cm

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6 cm

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8 cm

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Solution

The correct option is C
6 cm

$In Δ A B C$

$XY || BC (Given)$

$\frac{A X}{X B}$ = $\frac{A Y}{Y C} . . . (i)$
$(By Basic Proportionality Theorem)$

$Given: A B = 4 B X \Rightarrow A X + B X = 4 B X \Rightarrow A X = 3 B X \Rightarrow \frac{A X}{X B} = \frac{3}{1}$

$Substituting this in (i), we get \frac{A Y}{Y C} = \frac{3}{1} = \frac{A Y}{2}$ = $\frac{3}{1}$

$\Rightarrow A Y = 6 c m$

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

The correct option is C 6 cm In Δ ABC XY || BC (Given) AXXB =AYYC...(i) (By Basic Proportionality Theorem) Given: AB=4BX⇒AX+BX=4BX⇒AX=3BX⇒AXXB=31 Substituting this in (i), we getAYYC=31=AY2 = 31 ⇒ AY=6 cm

$XY is drawn parallel to the base BC of a Δ A B C cutting AB at X and AC at Y. If AB = 4 cm, BX and YC = 2 cm,$
$then find the measure of AY .$