Quadrilateral PQRS is a parallelogram such that its diagonals PR = QS = 8 cm, measure of angle PSR = 90 degrees, measure of angle QSR = 30 degrees. What is the perimeter of quadrilateral PQRS?

1 Answer
Dec 19, 2016

8(1+sqrt3)

Explanation:

If a parallelogram has a right angle, then it is a rectangle.

Given that anglePSR=90^@, PQRS is a rectangle.

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Given angleQSR=30^@, anglePSR=90^@, and PR=QS=8,

=> QR=8sin30=8*1/2=4=PS
=> SR=8cos30=8*sqrt3/2=4sqrt3=PQ
Perimeter PQRS=2*(QR+PQ)=2*(4+4sqrt3)=8(1+sqrt3)