Question

$\text{XY is drawn parallel to the base BC of a}\Delta ABC\text{cutting AB at X and AC at Y. If}\text{AB = 4 cm, BX and YC = 2 cm,}$
$\text{then find the measure of AY .}$

• A. 2 cm
• B. 4 cm
• C. 6 cm
• D. 8 cm

Answer 1

The correct option is C

6 cm

$\text{In}\Delta ABC$

$\text{XY || BC (Given)}$

$\frac{AX}{XB}$ =$\frac{AY}{YC}...\left(i\right)$
$\text{(By Basic Proportionality Theorem)}$

$\text{Given:}AB=4BX\Rightarrow AX+BX=4BX\Rightarrow AX=3BX\Rightarrow \frac{AX}{XB}=\frac{3}{1}$

$\text{Substituting this in (i), we get}\frac{AY}{YC}=\frac{3}{1}=\frac{AY}{2}$ = $\frac{3}{1}$

$\Rightarrow AY=6cm$