SOLUTION: A rectangle has a length that is 2 less than 3 times the width, if the area of this rectangle is 16, Find the dimensions and the perimeter

Question 813791: A rectangle has a length that is 2 less than 3 times the width, if the area of this rectangle is 16, Find the dimensions and the perimeter

Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
L = 3w - 2
a = Lw = 16
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Lw = 16
(3w - 2)w = 16
3ww - 2w = 16
3ww - 2w - 16 = 0
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the above quadratic equation is in standard form, with a=3, b=-2, and c=-16
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to solve the quadratic equation, plug this:
3 -2 -16
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic equation has two real roots:
root 1: 2.66666667 = 2 + 2/3 = 8/3
root 2: -2
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Answer 1:
the negative root doesn't make sense for a length, so use the positive root:
w = 8/3
L = 3w - 2
L = 3(8/3) - 2
L = 8 - 2
L = 6
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Answer 2:
p = 2L + 2w
p = 2(6) + 2(8/3)
p = 12 + (16/3)
p = (36/3) + (16/3)
p = 52/3
p = 17.333333 = 17 + 1/3
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