Question

In the adjoining figure, all measurements are indicated in centimeter. Find the length of AO if $AX=9.5$ cm.

• A. 6.75 cm
• B. 9.25 cm
• C. 4.25 cm
• D. 4.75 cm

Answer 1

The correct option is D 4.75 cm

Since $D$ and $E$ are mid points of $AB$ and $AC$ respectively.

$DE\parallel BC$

In $△ADO$ and $△ABX$

$\angle OAD=\angle XAB$ (common angle)

$\angle ODA=\angle XBA$ (corresponding angles)

$\angle AOD=\angle AXB$ (corresponding angles)

So, $△ADO\parallel △ABX$ ($AAS$ criteria)

Using $BPT,$ we get $\frac{AO}{AX}=\frac{AD}{AB}=\frac{4}{8}$

So, $AO=\frac{4}{8}\times AX=4.75cm$