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

 

 Apr 1, 2021
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If the perimeter of PQRS is 24, then PS = QR  = (24 - 14)/ 2 = 10/2 = 5

And the area would be the ST x PS = 28

So  ST x 5 = 28    divide both sides by 5

ST = 28/5  = 5.6  

And RT =√[RS^2 - ST^2] =    √[7^2 - 5.6^2 ] = √17.64   = 4.2

So RT + QR  = 4.2 + 5 = 9.2 =  QT

So the perimeter of  rectangle QOST =  2(ST + QT)  = 2(5.6 + 9.2)  = 29.6 units

 

 

cool cool cool

 Apr 1, 2021

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