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Points X, Y, and Z are on the sides QR , PR, and PQ respectively, of right triangle PQR  such that PZXY is a square. If PQ=10 and PR=10, then what is the side length of the square?

 Mar 21, 2023
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What is the side length of the square?

 

Hello Guest!

 

The segment QR is the hypotenuse in the triangle PQR.

P is the origin of the coordinate system.

 

\(\color{blue}y=-x+10\\ \underline{x=y}\\ y=-y+10\\ 2y=10\\ \color{blue}y=5\\ \color{blue}x=5\\\)

The side length of the square is 5.

laugh  !

 Mar 21, 2023
edited by asinus  Mar 21, 2023

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