PQRS is a rectangle in which PQ=2PS. T and U are the midpoint of PS and PQ respectively. QT and US intersect at V, Then Ar(QRSV)/ar(PQT)=

My friend , u are slightly mistaken. We have to find ar(QRSU)/ar(PTQ). YOU SHOULD BE CLEAR WITH THE DIAGRAM. therefore area of triangle PTQ. = 1/2×PQ×PT.  As we know that PQ = 2PS and PT=PS/2. therefore ar of triangle PTQ = 1/2×2PS×PS/2 = (PS^2/2). Now QRSU is a Trapezium .. is area should be 1/2(QU+RS)×QR. we know that QU=1/2PQ=PS and RS=PQ=2PS. Therefore ar(QSRU) =1/2(PS+2PS)×PS = (3PS^2/2). NOW AR(QSRU)/(PQT) = (3PS^2/2)/(PS^2/2) = 3. Hope u understand.