Answer:
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:
[tex]3a+4b=50\\a=\frac{50-4b}{3}[/tex]
The area of one rectangle is a× b, therefore for the two rectangles, the area is given as:
[tex]A=2(a*b)\\Substituting:\\A=2(\frac{50-4b}{3} )(b)\\A=\frac{100b-8b^2}{3}[/tex]
At maximum area, dA/db = 0
[tex]A=\frac{100b-8b^2}{3}\\\\\frac{dA}{db}= \frac{100}{3}-\frac{16b}{3} \\at\ maximum\ area\ dA/db=0\\0=\frac{100}{3}-\frac{16b}{3} \\\frac{100}{3}=\frac{16}{3}b\\16b=100\\b= 100/16=6.25\ yard \\[/tex]
Substituting b to find a
[tex]a=\frac{50-4b}{3}\\a=\frac{50-4(6.25)}{3}=25/3=8.33[/tex]
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
