Aphysical education teacher is planning to outline two adjacent identical rectangular areas for a new game that students will be learning. if the boundaries, including the center line, of this "court" must be marked with a 505050 yard roll of tape, what is the maximum area of one of the smaller rectangular spaces, rounded to the nearest tenth of a square yard?

The maximum area of one small rectangle would be 50yd².

Outlining both the outer boundaries as well as the center line means there are essentially 5 sides to be outlined by tape.  When maximizing area and minimizing perimeter, we make the sides as close to equilateral as possible.  50/5 = 10 yards per side.  This means the width on both ends would be 10, the center line would be 10, and the total length of both courts put together would be 10.  However to find the area of one small rectangle, we would divide that length in half; we would use a width of 10 and a length of 5.  The area would then be 10(5)=50.