To solve this problem, we need to remember that the perimeter of a rectangle can be found using the formula: P = 2 (l + w) where the variable l represents the length of the rectangle and the variable w represents the width of the rectangle.
We know that the length of the field is 5 yards less than double the width, or 2w-5. We can substitute this value into our formula for the variable l (length).
P = 2 (w + 2w - 5)
Now, we can substitute the value for the perimeter (284) into the equation for the variable p.
284 = 2 (w + 2w - 5)
Next, we should simplify what is inside the parentheses by adding together the like terms.
284 = 2(3w - 5)
Next, we should divide both sides of the equation by 2.
142 = 3w - 5
After that, we can add 5 to both sides of the equation.
147 = 3w
Finally, we should divide both sides of the equation by 3 to get the variable w alone on the right side of the equation.
w = 49
Therefore, the width of the rectangle is 49. We know that the length is 5 yards less than double the width, or 2w - 5. To solve for the length, we should substitute in our value for the width and simplify.
l = 2w - 5
l = 2(49) - 5
l = 98 - 5
l = 93
Therefore, the width of the rectangle is 49 yards and the length of the rectangle is 93 yards.
Hope this helps!