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

In a parallelogram \(PQRS\), \(SR = PQ\) and \(QR=PS\).

Step2: Calculate the perimeter formula

The perimeter \(P\) of a parallelogram is \(P = 2(SR + QR)\).

Step3: Substitute the given values

Given \(SR = 4\sqrt{2}\) and \(QR=\sqrt{10}\). Then \(P=2(4\sqrt{2}+\sqrt{10})\).
Using the distributive property \(a(b + c)=ab+ac\), we have \(P = 8\sqrt{2}+2\sqrt{10}\).

Answer:

\(8\sqrt{2}+2\sqrt{10}\) units (the second option).