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?

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Answer 1 · 2016-12-19T01:28:17

#8(1+sqrt3)#

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)#