Question

in the diagram, ( sr = 4sqrt{2} ) and ( qr = sqrt{10} ). what is the perimeter of parallelogram ( pqrs )?
( sqrt{10} ) units
( 8sqrt{2}+2sqrt{10} ) units
( 16sqrt{2} ) units
( 8sqrt{2}+8 ) units

Explanation:

Step1: Recall the property of parallelogram perimeter

In a parallelogram, \(PQ = SR\) and \(QR = PS\). The perimeter \(P\) of a parallelogram is \(P = 2(SR + QR)\).

Step2: Substitute the given values of \(SR\) and \(QR\)

Given \(SR = 4\sqrt{2}\) and \(QR=\sqrt{10}\). Then \(P=2(4\sqrt{2}+\sqrt{10})=8\sqrt{2} + 2\sqrt{10}\).

Answer:

\(8\sqrt{2}+2\sqrt{10}\text{ units}\)