The required perimeter of parallelogram PQRS is [tex]8\sqrt{2} + 2\sqrt{10}[/tex] units.
Given that,
On a coordinate plane, parallelogram PQRS,
There points are P is at (-2, 5), point Q is at (2, 1), point R is at (1, -2), and point S is at (-3, 2),
Length of SR = [tex]4\sqrt{2}[/tex] and QR = [tex]\sqrt{10}[/tex].
We have to find,
The perimeter of parallelogram PQRS.
According to the question,
The properties of the parallelogram is each two opposite sides are parallel
and each two opposite sides are equal.
Its perimeter is the twice the sum of two adjacent sides
Then, PQRS is a parallelogram,
SR and RQ are two adjacent sides,
The perimeter of parallelogram PQRS = 2(RQ + SR)
The perimeter of parallelogram PQRS = [tex]2 ( 4\sqrt{2} + \sqrt{10} )[/tex]
The, The perimeter of parallelogram PQRS = [tex]8\sqrt{2} + 2\sqrt{10}[/tex].
Hence, The required perimeter of parallelogram PQRS is [tex]8\sqrt{2} + 2\sqrt{10}[/tex] units.
For the more information about Parallelogram click the link given below.
https://brainly.com/question/15771657.
