Question

In $△ABC,XY\parallel BC,\frac{AY}{CY}=\frac{1}{2}$ and $AX=4$. Find $BX$.

Answer 1

Given that:

In $△ABC,XY\parallel BC,\frac{AY}{CY}=\frac{1}{2}$ and $AB=4$

To find:

$BX=?$

Solution:

Since, $\frac{AY}{CY}=\frac{1}{2}$

$\therefore \frac{AY}{AC}=\frac{1}{3}$

Now, $XY\parallel BC$

$\therefore △AXY\sim △ABC$

or,, $\frac{AY}{AC}=\frac{AX}{AB}$

or, $\frac{1}{3}=\frac{4}{AB}$

or, $AB=12$

$\therefore BX=AB-AX=12-4=8$