Final answer:
To find a rectangular park with the same perimeter but a smaller area than the original 55 yards by 105 yards, one could choose new dimensions such as a width of 60 yards and a length of 100 yards. This results in a park with a smaller area of 6000 square yards compared to 5775 square yards for the original park.
Step-by-step explanation:
The subject of the question is Mathematics, specifically focusing on geometry and scale drawings. The grade level of this question is Middle School.
If we have a rectangular park that is 55 yards wide and 105 yards long, we know the perimeter is 2*(55 + 105) = 320 yards. To find the dimensions of another rectangular park with the same perimeter but a smaller area, the width and length must have a smaller product than 55*105. Let's choose a new width of 60 yards (5 yards larger than the original), then calculate the new length:
Total perimeter = 320 yards still applies
320 yards = 2*(width + length)
160 yards = width + length (divide both sides by 2)
160 yards - width = length
160 yards - 60 yards = 100 yards (the new length)
The new park would have a width of 60 yards and a length of 100 yards. The area of the new park is 60 yards * 100 yards = 6000 square yards, which is less than the original area of 5775 square yards (55 yards * 105 yards).