# The length of a rectangular field is 20 less than its width. The area of the field is 12,000 ft2. What is the width of the field

The answer is 120 feet. The area of the field (A) is: A = w · l (w - width, l - length) It is known: A = 12,000 ft² l = w - 20 So, let's replace this in the formula for the area of the field: 12,000 = w · (w - 20) 12,000 = w² - 20 ⇒ w² - 20w - 12,000 = 0 This is quadratic equation. Based on the quadratic formula: ax² + bx + c = 0 ⇒ [latex]x= \frac{-b+/- \sqrt{ b^{2}-4ac } }{2a } [/latex] In the equation w² - 20w - 12,000 = 0, a = 1, b = -20, c = -12000 Thus: [latex]w= \frac{-(-20)+/- \sqrt{(-20)^{2}-4*1*(-12000) } }{2*1} = \frac{20+/- \sqrt{400+48000} }{2} = \frac{20+/-220}{2} [/latex] So, width w can be either [latex]w= \frac{20+220}{2}= \frac{240}{2}=120 [/latex] or [latex]w= \frac{20-220}{2}= \frac{-200}{2} =-100[/latex] Since, the width cannot be a negative number, the width of the field is 120 feet.