Question

IN the figure, PQRS is a parallelogram. If X and Y are mid points of PQ and SR respectively and diagonal SQ is joined, the ratio $ar\left(||gmXQRY\right):ar\left(△QSR\right)$=

• A. 1: 4
• B. 2:1
• C. 1: 2
• D. 1:1

Answer 1

The correct option is D

1:1

In ||gm PQRS, X and Y are the mid points of PQ and SR respectively. Now, XY and SQ are joined.
$\because XY$ bisects PQ and SR
$\therefore PXYSandXQRY$ are also ||gms
and $ar\left(△PXYS\right)=ar\left(△XQRY\right)$
$\because ||gmPQRSand△QSR$ are on the same base and between the same parallel lines
$\therefore ar\left(△QSR\right)=\frac{1}{2}ar\left(||gmPQRS\right)$
But $ar\left(||gmXQRY\right)=\frac{1}{2}ar\left(||gmPQRS\right)\therefore ar\left(||gmXQRY\right)=ar\left(△QSR\right)\Rightarrow \frac{ar\left(||gmXQRY\right)}{ar\left(△QSR\right)}=1:1$