Question

In the figure, $\overline{XY}||BC$
AX = 1 cm
XB = 3 cm
BC = 6 cm
then XY = ................

• A. 2 cm
• B. 1.5 cm
• C. 1 cm
• D. 3 cm

Answer 1

Answer: (B)

1.5 cm

Given $\overline{XY}||\overline{BC}$

In $△AXY$ and $△ABC$,

$\angle XAY=\angle BAC$ ....... [Same vertex]

$\angle AXY=\angle ABC$ and $\angle AYX=\angle ACB$ ...... $[\because XY\parallel BC]$

$\therefore △AXY\sim △ABC$ ........ [By AAA criterion]
$\therefore \frac{AX}{AB}=\frac{XY}{BC}$ .........$\left(i\right)$ (Corresponding sides of similar triangle are proportional)
Now, $AB=AX+XB=1+3=4$

$⟹AB=4$
$\therefore \frac{1}{4}=\frac{XY}{6}$ ........ From $\left(i\right)$

$\therefore XY=\frac{6}{4}$
$\therefore XY=1.5cm$

Hence, the answer is $1.5$ cm.