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

`8√(2)+2√(10)`

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√(2))+2(√(10))\\P=8√(2)+2√(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.

Answer 2

The perimeter is
`(8√(2)+2√(10))\ units`

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=√(10)\ units`

`SR=4√(2)\ units`

substitute in the formula of perimeter

`P=2(4√(2))+2(√(10))`

`P=(8√(2)+2√(10))\ units`