question_answer

In a \[\Delta ABC,\] XY is drawn parallel to BC, cutting sides at X and Y, where AB = 4.8 cm, BC = 7.2 cm and BX = 2 cm. What is the length of XY?

A) 4 cm

B) 4.1 cm

C) 4.2 cm

D) 4.3 cm

Correct Answer: C

Solution :

[c] Given that, \[AB=4.8\,cm,\] \[BC=7.2\,cm\]and \[BX=2\,cm\] \[\therefore \]      \[AX=AB-BX=4.8-2=2.8\,cm\] From figure, \[\Delta \Alpha XY\approx \Delta ABC\] \[\therefore \]      \[\frac{XY}{BC}=\frac{AX}{AB}\] \[\Rightarrow \]   \[XY=\frac{2.8}{4.8}\times 7.2\] \[\therefore \]      \[XY=4.2\,cm\]