Problem Analysis:
- We are given that it takes 64 minutes to mow down an equilateral triangle-shaped field.
- We need to find the additional time required to mow down the same triangle-shaped field when each side is increased by 37.5%.

Solution:
To solve this problem, we can break it down into the following steps:

Step 1: Calculate the area of the original equilateral triangle:
- The area of an equilateral triangle can be calculated using the formula:
Area = (sqrt(3) / 4) * side^2
- Since the triangle is equilateral, all three sides are equal. Let's assume the side length of the original triangle is 's'.

Step 2: Calculate the side length of the new triangle:
- The side length of the new triangle is increased by 37.5%.
- To calculate the new side length, we can multiply the original side length by 1.375.

Step 3: Calculate the area of the new triangle:
- Using the formula mentioned in Step 1, we can calculate the area of the new triangle using the new side length.

Step 4: Calculate the additional time required:
- Since the original triangle took 64 minutes to mow, we can assume that it takes 1 minute to mow down 1 unit of area.
- Therefore, the additional time required to mow the new triangle can be calculated by subtracting the area of the original triangle from the area of the new triangle.

Step 5: Convert the additional time to minutes:
- Since the additional time is expressed in terms of the number of units of area, we need to convert it to minutes.
- Since it takes 1 minute to mow down 1 unit of area, the additional time required in minutes will be equal to the additional time calculated in Step 4.

Step 6: Calculate the final answer:
- Calculate the additional time required using the steps mentioned above.
- The correct answer is given as '57', so we need to verify if our calculations match this answer.

Conclusion:
By following the above steps, we can calculate the additional time required to mow the triangle-shaped field with each side increased by 37.5%.