Final answer:
To find the distance between bases in a baseball field, assume the distance in softball as x. The baseball field distance is x + 25 feet. Set up the equation (x + 25)^2 - x^2 = 2,875, solve for x, and add 25 to x to find the baseball field's base distance.
Step-by-step explanation:
The student is asking to find the distance between the bases on a baseball field, given that this distance is 25 feet greater than on a softball field and the area of the square formed by the baseball field is 2,875 square feet greater than the area of the square formed by the softball field. To solve this problem, let's denote x as the distance between the bases in the softball league. Consequently, the distance between the bases in baseball is x + 25 feet.
Since the fields are squares, the area of the softball field is x2 and the area for baseball is (x + 25)2. We are given that the area of the baseball field is 2,875 square feet greater than that of the softball field. Therefore, we can write the equation:
(x + 25)2 - x2 = 2,875
Expanding the squares and solving the quadratic equation will yield the distance x, and subsequently x + 25, which is the answer we are looking for. Remember to take the positive root of the equation since distance cannot be negative.