Answer: Thus, the width of the second park is 92.5 yards, and its length is also 92.5 yards.
Step-by-step explanation: The perimeter of the first rectangular park is:
P = 2L + 2W
P = 2(110 yds) + 2(75 yds)
P = 220 yds + 150 yds
P = 370 yds
Since the second rectangular park has the same perimeter as the first, its perimeter is also 370 yards. Let's call its width "x" and its length "y".
Then, we have:
2x + 2y = 370
Simplifying this equation, we get:
x + y = 185
The area of the second park is:
A = xy
To find the dimensions of the second park with the largest area, we need to maximize this expression subject to the constraint x + y = 185.
One way to do this is to use the method of Lagrange multipliers. However, in this case, we can use a simpler approach based on the fact that the area of a rectangle is maximized when its sides are equal. Therefore, we can set x = y = 185/2 = 92.5.