Final answer:
To solve the word problem, set up a linear equation using the given information. Substitute the given perimeter into the equation and solve for the width. Then, find the length by adding 25 to the width.
Step-by-step explanation:
To solve the word problem and find the length, we can set up a linear equation based on the given information. Let's call the width of the field 'w'. According to the problem, the length is 25 meters longer than the width, so the length would be 'w + 25'. The perimeter of a rectangle is equal to two times the length plus two times the width, so we can write the equation as follows:
2(w + 25) + 2w = perimeter
Now we can substitute the given perimeter into the equation and solve for 'w'. Once we find 'w', we can calculate the length by adding 25 to it.
For example, if the given perimeter is 100 meters, we would have:
2(w + 25) + 2w = 100
Simplifying the equation gives us:
4w + 50 = 100
Subtracting 50 from both sides:
4w = 50
Dividing both sides by 4:
w = 12.5
Therefore, the width of the field is 12.5 meters. To find the length, we add 25 to the width:
Length = 12.5 + 25 = 37.5 meters