anonymous
  • anonymous
the length fo a rectangle is four greater than the width,the are is sixty. find the length & with of the rectangle?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Since we're told that the length is four greater than the width, x = Width, x+4 = Length The area of a rectangle is L*W, so (x)(x+4) = \[x^{2} + 4x\] You're given that the area is 60, so \[x^{2} + 4x = 60\] Move all of your terms to one side to solve: \[x^{2} + 4x - 60 = 0\] Find the roots of your quadratic equation: \[(x+10)(x-6) = 0\] So you have roots x = -10 and x = 6 It's impossible to have a length or width that's negative, so reject x = -10 In the beginning, we set x = width; we just calculated x to be 6, so the width = 6 The length is four greater than the width, so the length is x + 4 = 6 + 4 = 10.

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