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In the diagram, two pairs of identical isosceles triangles are cut off of square $ABCD$, leaving rectangle $PQRS$. The total area cut off is $200 \text{ m}^2$. What is the length of $PR$, in meters?

 Mar 3, 2021
 #1
avatar+564 
+2

we can use pythagorean theorum to solve this problem, so PR^2 = PS^2+SR^2.

 

those two lengths are the hypotenuses of triagnles APS and SDR, so

 

PS^2+SR^2 = 2AP^2+2SD^2.

 

we also know that AP^2+SD^2=200, so AP^2+2SD^2=2(200)=400.

 

this means that PR^2=400, so PR=$\boxed{20}$

 Mar 3, 2021
edited by SparklingWater2  Mar 3, 2021
 #3
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Your method is right!!!

 

I was guesstimating... laugh

jugoslav  Mar 3, 2021
 #2
avatar+1486 
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PB => x         AP => 2x         AB => 3x

 

x2 + (2x)2 = 200          x = 2√10

 

PR = sqrt[x2 + (3x)2] = √400 = 20   

 Mar 3, 2021

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