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in the figure below,  PQRS is a parallelogram of perimeter  24 and area of 28 What is the perimeter of rectangle  QOST? Include an explanation of how you solved the problem

 Dec 3, 2018
 #1
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Since SR parallel to PQ....they are equal

 

So....to find PS = QR we have

 

24 - 2SR = PS + QR

24 -2(5) = PS + QR

24 - 10 = PS + QR

14 = PS + QR

 

So  QR = 7 = PS

 

And the area of the parallelogram PQRS =  QR * ST

 

So

 

28 = 7 * ST    divide both sides by 7

 

4 = ST = OQ

 

And using the Pythagorean Theorem

RT =  sqrt [ RS^2 - ST^2] =  sqrt [ 5^2 - 4^2] = sqrt [ 25 - 16] = sqrt[9] = 3 = OP

 

So....the perimeter of QOST =

 

2 (OP + PS) + 2(ST) =

 

2 (3 + 7) + 2(4) =

 

2*10 + 2*4 =

 

28 units

 

 

cool cool cool

 Dec 3, 2018

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