Question

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

Answer 1

B

Explanation:

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Answer 2

Since the figure is a parallelogram, then SP=RQ, and SR=PQ.

To find SR, we draw right triangle SAR, as shown in the picture, where the coordinates of A are clearly (-3, -2).

Thus, we can see that SA=4 units, and AR=4 units. By the Pythagorean theorem,

`SR= √(4^2+4^2)= √(2\cdot4^2)=4 √(2).`


Similarly, to find SP, which is equal to QR, we draw the triangle PBS, where the coordinates of B are (-2, 2).

Clearly, PB=3 and SB=1, thus using the Pythagorean theorem in right triangle PBS:


`SP= √(1^2+3^2)= √(10)` units.


The perimeter of the parallelogram is SP+RQ+SR+PQ=



`√(10) +√(10) +4 √(2)+4 √(2)=2√(10) +8 √(2)`.



Answer: second choice