Solution:
Consider the following diagram of the rectangular field:
The perimeter P of a polygon is the sum of its sides, thus we can express the perimeter of the given rectangular field as:
[tex]P\text{ = 2W + 2L }[/tex]where P = 312 yards, L = 83 yards, and L is unknown. Then, replacing the given data into the previous equation, we get:
[tex]312\text{ = 2(W) + 2(83)}[/tex]this is equivalent to:
[tex]312\text{ = 2(W) + }166[/tex]solving for 2W, we get:
[tex]2W\text{ = 312 - 166 = 146}[/tex]solving for W, we get:
[tex]W\text{ = }\frac{146}{2}=\text{ 73}[/tex]we can conclude that the correct answer is:
The width of the rectangular field is 73 yards.
