Mathematics
dylex323
25

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

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(1) Answers
MorganTyyler

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.

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