in the diagram, sr = 4√2 and qr = √10. what is the perimeter of parallelogram pqrs?\n√10 units\n8√2 + 2√10…

Explanation:

Step1: Identify the lengths of adjacent sides.

The problem states that the lengths of two adjacent sides of the parallelogram PQRS are $SR = 4\sqrt{2}$ and $QR = \sqrt{10}$.

Step2: Recall the properties of a parallelogram.

In a parallelogram, opposite sides are equal in length. Therefore, $PQ = SR = 4\sqrt{2}$ and $PS = QR = \sqrt{10}$.

Step3: Calculate the perimeter of the parallelogram.

The perimeter $P$ of a parallelogram is given by the formula $P = 2 \times (\text{length of one side} + \text{length of adjacent side})$. $$P = 2(SR + QR)$$ Substitute the given values: $$P = 2(4\sqrt{2} + \sqrt{10})$$ $$P = 8\sqrt{2} + 2\sqrt{10}$$

Answer:

B. $8\sqrt{2} + 2\sqrt{10}$ units