Solution below.

Reveal solution by highlighting:

As the 2 red sides have been constructed in the same way, they are the same length: a. 2a = 50. Let the vertical blue line be b. The horizontal blue line will be 50-b, and half of that is 25-b/2.

Pythagoras (among others) tells us, b²+(25-b/2)² = 25²

<=> b²+25²-25*b+b²/4 = 25²

<=> (1+1/4)b²-25*b = 0

<=> b²-20*b = 0

<=> b(b-20) = 0

<=> b = 0 or b = 20. 0 won’t work, then we wouldn’t have a true rectangle with a positive area. So b = 20, a = 25. 50-b = 30. The area of the rectangle is b*(50-b) = 20*30 = 600.