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n the figure below, PQRS is a parallelogram of perimeter  26 and area 28. What is the perimeter of rectangle QOST?

 

 Nov 17, 2020
 #1
avatar+1062 
-1

perimeter is 28       sides of triangle STR are 3-4-5     PS = 28 / ST = 7

 Nov 17, 2020
edited by Guest  Nov 17, 2020
 #2
avatar+116125 
+2

Since SR = 5   then so is  QP

And since the perimeter of  PQRS  is 26, then QR =  (26 - 10) / 2 = 16/2   = 8 

 

And the  area  of PQRS  =   QR * ST

So

28 = 8 * ST

28/8 = ST

7/2  = ST  = 3.5

 

And using the Pythagorean Theorem

 

RT^2 + ST^2  = RS^2

RT^2  + (3.5)^2 =  5^2

RT^2  = 5^2 - 3.5^2

RT^2  = 25 - 12.25

RT^2 = 12.75

RT = sqrt (12.75)

 

Perimeter of QOST =   2 ( QR + RT + ST)  =  2 ( 8  + sqrt (12.75)  + 3.75)  = 

23 + 2sqrt (12.75)

 

 

cool cool cool

 Nov 17, 2020
 #3
avatar+1062 
0

wrong answer!!!cheeky and the first answer is incorrect too!!!cool

Where was my head?!?cool

jugoslav  Nov 17, 2020
edited by jugoslav  Nov 17, 2020
edited by jugoslav  Nov 17, 2020
 #4
avatar+116125 
0

Sorry, jugoslav.....we are not  given any info as to what  the length of  legs RT and ST might be....we cannot assume that  this is a 3-4-5 right  triangle

 

 

cool cool cool

CPhill  Nov 17, 2020
 #5
avatar+1062 
0

You are absolutely right, Phill! I don't know what happened but I didn't see this: "PQRS is a parallelogram of perimeter  26". My focus was on a triangle STR, and I assumed that that triangle was 3-4-5

jugoslav  Nov 17, 2020

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