Question

In the diagram, SR = and QR = . What is the perimeter of parallelogram PQRS?

A. √10 units
B. 8√2 + 2√10 units
C. 16√2 units
D. 8√2 + 8 units

Answer 1

B.
`8\sqrt2+2√(10)` units

Explanation:

We are given that a parallelogram PQRS in which point P(-2,5), Q(2,1),R(1,-2) and S(-3,2).

We have to find the perimeter of parallelogram PQRS.

Distance formula :
`√((x_2-x_1)^2+(y_2-y_1)^2)`

Using the formula

`SR=√((1+3)^2+(-2-2)^2)=4\sqrt2`units

`QR=√((1-2)^2+(-2-1)^2)=√(10) units`

Now, the perimeter of parallelogram =2(SR+QR)

The perimeter of parallelogram =
`2(4\sqrt2+√(10))=8\sqrt2+2√(10) units`

Answer:B.
`8\sqrt2+2√(10)` units