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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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

$8 (1 + \sqrt{3})$ $8(1+sqrt3)$

Explanation:

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

Given that $∠ P S R = 90^{\circ}, P Q R S$ $anglePSR=90^@, PQRS$ is a rectangle.

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Given $∠ Q S R = 30^{\circ}, ∠ P S R = 90^{\circ}$ $angleQSR=30^@, anglePSR=90^@$ , and $P R = Q S = 8$ $PR=QS=8$ ,

$\Rightarrow Q R = 8 sin 30 = 8 \cdot \frac{1}{2} = 4 = P S$ $=> QR=8sin30=8*1/2=4=PS$
$\Rightarrow S R = 8 cos 30 = 8 \cdot \frac{\sqrt{3}}{2} = 4 \sqrt{3} = P Q$ $=> SR=8cos30=8*sqrt3/2=4sqrt3=PQ$
Perimeter $P Q R S = 2 \cdot (Q R + P Q) = 2 \cdot (4 + 4 \sqrt{3}) = 8 (1 + \sqrt{3})$ $PQRS=2*(QR+PQ)=2*(4+4sqrt3)=8(1+sqrt3)$

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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

Explanation:

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