Question

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

Answer 1

Answer:

The perimeter is $(8\sqrt{2}+2\sqrt{10})\ units$

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

$P=2SR+2QR$

we have

$QR=\sqrt{10}\ units$

$SR=4\sqrt{2}\ units$

substitute in the formula of perimeter

$P=2(4\sqrt{2})+2(\sqrt{10})$

$P=(8\sqrt{2}+2\sqrt{10})\ units$

Answer 2

Answer:

$8\sqrt{2}+2\sqrt{10}$

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 $SR=PQ$ and $PS=QR$.

So, the perimeter would be:

$P=SR+QR+PQ+PS=SR+QR+SR+QR=2SR+2QR\\P=2(4\sqrt{2})+2(\sqrt{10})\\P=8\sqrt{2}+2\sqrt{10}$

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.