Question

In the given figure, $XY\parallel BC$. Given that $AX=3cm$, $XB=1.5cm$ and $BC=6cm$. Calculate: $XY$

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

Answer 1

The correct option is A $4cm$

In $△AXY$ and $△ABC$

$\angle XAY=\angle BAC$ (Common angle)

$\angle AXY=\angle ABC$ (Corresponding angles for parallel lines XY and BC)

$\angle AYX=\angle ACB$ (Corresponding angles for parallel lines XY and BC)

Thus, $△AXY\sim △ABC$ (AAA rule)

Hence, $\frac{AB}{AX}=\frac{AC}{AY}=\frac{BC}{XY}$ (Corresponding sides)

$\frac{3+1.5}{3}=\frac{6}{XY}$

$XY=\frac{3\times 6}{4.5}$

$XY=4cm$