Question

A rectangular field has a length that is 90 feet more than twice the width of the field. If the area of the field is 58,500 square feet, what is the width of the field A. 390 feet B. 201 feet C. 132 feet D. 150 feet

Answer 1

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.