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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.

 

 
SmartMathMan  Dec 7, 2017
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 #1
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If the permeter of PQRS  is 24....remember that PQ  = SR   and   PS  = QR

 

So...... PQ  + SR  +  PS + QR  = 24

 

5  +  5    + PS + QR   =   24       sub  PS for QR

 

10  +  PS  + PS  =  24       subtract 10 on each side

 

2PS  =   14     divide both sides by 2

 

PS  = 7  = QR

 

And the area of PQRS   =  PS  * height of PQRS (=ST)  ......so we have that

 

28  = 7 * ST    divide both sides by 7

 

4  = ST

 

And since RST is a right triangle.... using the Pythagorean Theorem...

 

 RS^2 - ST^2  =  RT^2

 

5^2  - 4^2  = RT^2

 

25  - 16  = RT^2

 

9  = RT^2      take the square root of both sides

 

3  = RT

 

So........QT  = QR + RT  =    PS + RT  =    7 + 3   = 10

 

So...the perimeter of  QOST  =  2 [ QT + ST]  = 2 [ 10 +  4]  =  2 * 14  =  28

 

 

 

cool cool cool

 
CPhill  Dec 7, 2017
 #2
avatar+79 
0

thx so much man

 
SmartMathMan  Dec 7, 2017

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