Middle School Madness

Weekly problems for middle school students ready for a challenge. These puzzles enhance logical thinking and make math exciting and rewarding.

A right triangle has a perimeter of 84 centimeters. The altitude drawn from the right-angle vertex to the hypotenuse divides the hypotenuse into two segments whose lengths are in the ratio 9:16.  

A square is placed inside the right triangle so that: 
One vertex of the square is at the right-angle vertex. 
Two sides of the square lie along the legs of the triangle. 
The opposite vertex touches the hypotenuse. 
What is the area of the square?

 


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