Answer:
D. 150 feet
Step-by-step explanation:
The formula for the area of a rectangle is: area = lw, where l = length and w = width. In this case, the length is defined as '90 feet more than twice the width' or l = 2w + 90. If we put this expression in for the value of 'l' in our formula for area we get:
area = w(2w +90), distribute: area = 2w² + 90w = 58500
Subtracting 58500 from both sides, we get the following polynomial:
2w² + 90w - 58500
We can divide all the terms by '2' to simplify:
w² + 45w - 29250
Next, we look for the two factors of 29,250 that will add up to 45, which is -150 and +190 to factor our polynomial:
(w - 150)(w + 190) = 0
Setting both equations equal to 0 and solving for w:
w - 150 = 0 or w = 150
w + 190 = 0 or w = -190
Since our with can not be negative, then the correct width of the field is 150 ft.
