Question

triangle congruence
in the diagram, sr = 4√2 and qr = √10. what is the perimeter of parallelogram pqrs?
8√2 + 2√10 units
8√2 + 8 units
16√2 units
√10 units

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite - sides are equal. So, \(SR = PQ = 4\sqrt{2}\) and \(QR=PS=\sqrt{10}\).

Step2: Calculate the perimeter formula

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

Step3: Substitute the values

Substitute \(SR = 4\sqrt{2}\) and \(QR=\sqrt{10}\) into the formula: \(P=2\times4\sqrt{2}+2\times\sqrt{10}=8\sqrt{2}+2\sqrt{10}\).

Answer:

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