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Help needed urgently

 

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?

 Apr 27, 2023
 #1
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+2

2. Theorem of rays

 

\(\overline {PR}:x=\overline {PQ}:(\overline {PQ}-x)\\ 10:x=10:(10-x)\\ 10x=10\cdot (10-x)\\ 10x=100-10x\\20x=100\\ \color{blue}x=5\)

 

The side length of the square is 5.

laugh  !

 Apr 27, 2023

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