Question

In the figure, $\square$ $PQRV$ is a trapezium in which seg $PQ$ $\parallel$ seg $VR$. $SR=4$ and $PQ=6$. Find $VR$.

• A. $(10+4\sqrt{3})$ units
• B. $4\sqrt{3}$ units
• C. $10$ units
• D. $\sqrt{3}$ units

Answer 1

The correct option is A $(10+4\sqrt{3})$ units

In $△QRS$, $SR=4$ cm and $\angle SQR={45}^o$ and $\angle QRS={90}^o$

Then in $△QRS$, we have

$\tan {45}^0=\frac{SR}{PQ}$

$\Rightarrow 1=\frac{4}{PQ}$

$\Rightarrow PQ=4$ cm

In trapezium $PQ||VR$, then $PQ=PT=4$ cm

In $△PTV$, $\angle TPV={60}^o$ and $PT=4$ cm

$\Rightarrow \tan {60}^0=\frac{VT}{PT}$

$\Rightarrow \sqrt{3}=\frac{VT}{4}$

$\Rightarrow VT=4\sqrt{3}$ cm

But $VR=VT+TS+SR$, where $PQ=TS=6$ cm ....given

$\Rightarrow VR=4\sqrt{3}+6+4=10+4\sqrt{3}$ cm