P, Q, R and S are the mid-points of the sides AB, BC, CD and DA of a rectangle ABCD. If each diagonal of the rectangle is 18 cm long, what is the perimeter of the quadrilateral PQRS?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 36 cm
By the mid-point theorem, the segment joining the mid-points of two sides of a triangle is half the third side. Each side of PQRS joins mid-points of two sides of a triangle cut off by a diagonal.
In \(\triangle ABC\): \(PQ=\frac{1}{2}AC=9\) cm; in \(\triangle ADC\): \(SR=\frac{1}{2}AC=9\) cm
In \(\triangle ABD\): \(PS=\frac{1}{2}BD=9\) cm; in \(\triangle CBD\): \(QR=\frac{1}{2}BD=9\) cm
Perimeter of PQRS \(=4\times9=36\) cm
