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Points $X$, $Y$, and $Z$ are on the sides $\overline{QR}$, $\overline{PR}$, and $\overline{PQ}$, respectively, of right triangle $PQR$ such that $PZXY$ is a square. If $PQ = 6$ and $PR = 6$, then what is the side length of the square?

 Apr 30, 2024
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Without  explanation.....the  side of the square = [ product of leg lengths ]  / [ sum of the leg lengths ]  =

 [6 * 6 ]  /  [ 6 + 6 ] = 36 / 12  =  3

 

I can show you how I got this  if you want me to.......

 

cool cool cool

 Apr 30, 2024

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