A physical 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 single 50-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?

52.1 yard²

Explanation:

Let us assume the length of the center line is a yards and the other side is b yards. Since it is two adjacent identical rectangle, from the diagram attached, the perimeter of the rectangle is:

3a + 4b = 50 yards

Making a the subject of the formula:

The area of one rectangle is a× b, therefore for the two rectangles, the area is given as:

At maximum area, dA/db = 0

Substituting b to find a

The maximum area of one of the rectangle = ab = 8.33 × 6.25 = 52.1 yard²

The maximum area of the two adjacent identical rectangle = 2ab = 104.2 yard²

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explanation: