Question

$PQRS$ is a rectangle in which $PQ=2PS$. $T$ and $U$ are the mid points of $PS$ and $PQ$ respectively, $QT$ and $US$ intersect at $V$. The area of $QRSV$ divided by the area of $PQT$ is

• A. $\frac{9}{7}$
• B. $\frac{7}{4}$
• C. $\frac{6}{5}$
• D. $3$

Answer 1

The correct option is D $3$

Given : $PQ=2PS$

$PT=\frac{PS}{2}$

$PU=\frac{Pq}{2}=PS$

$\Rightarrow$ Area of $PQT=\frac{1}{2}\times PT\times PQ$

$=\frac{1}{2}\times \frac{PS}{2}\times 2PS$

$=\frac{P{S}^2}{2}$

$\Rightarrow$ Area of $QRSV=\frac{1}{2}\times QR\times (SR+UQ)$

$=\frac{1}{2}\times PS(2PS+PS)$

$=\frac{3P{S}^2}{2}$

$\therefore \frac{AreaofQRSV}{AreaofPQT}=\frac{3P{S}^2}{2}÷\frac{P{S}^2}{2}$

$=3.$

Hence, the answer is $3.$