Question

Given a rectangle ABCD and P,Q,R,S mid-points of AB,BC,CD and DA respectively. If length of diagonal of rectangle is 8 cm , the quadrilateral PQRS is:

• A. Parallelogram with adjacent sides 4 cm and 8 cm
• B. Rhombus with side 4 cm
• C. Rectangle with adjacent sides 4 cm and 8 cm
• D. Square with side 4 cm

Answer 1

The correct option is B Rhombus with side 4 cm


The figure PQRS, formed by joining the mid points of the adjacent sides of a rectangle ABCD is a rhombus.
In $\Delta BCD$, the points Q and R are mid points sides BC and CD respectively.
$\therefore QR||DB$ (By mid-point theorem)
$QR=\frac{1}{2}DB$
$QR=\frac{1}{2}\left(8\right)$
$QR=4$
Hence, it is rhombus with side 4 cm.