On a coordinate plane, parallelogram p q r s is shown. point p is at (negative 2, 5), point q is at (2, 1), point r is at (1, negative 2), and point s is at (negative 3, 2). in the diagram, sr = 4 startroot 2 endroot and qr = startroot 10 endroot. what is the perimeter of parallelogram pqrs? startroot 10 endroot units 8 startroot 2 endroot + 2 startroot 10 endroot units 16 startroot 2 endroot units 8 startroot 2 endroot + 8 units

The perimeter is

Step-by-step explanation:

we know that

A parallelogram is a quadrilateral where both pairs of opposite sides are parallel and equal

so

In this problem

PS=QR ----> equation A

SR=PQ ----> equation B

The perimeter of parallelogram PQRS is

P=PQ+QR+SR+PS ----> equation C

substitute equation A and equation B in equation C

we have

substitute in the formula of perimeter

Step-by-step explanation:

The perimeter of a parallelogram is the sum of all sides, but this figure has two pair sides that are equal. So, from its definition we deduct that and .

So, the perimeter would be:

Therefore, the correct answer is the second option. The final expression of the perimeter cannot be added because they don't have similar roots that allow us to sum them.