Question 105084
Your answer is correct.
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The method is:
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Length = 5*w + 2
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Width = w
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Area = L * w = 65 sq cm
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Multiply L * w and set it equal to the area to get the equation:
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(L * w) = 65
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Substitute 5*w + 2 for L to change the equation to:
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(5w + 2)*w = 65
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Multiply out the left side:
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{{{5w^2 + 2w = 65}}}
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Subtract 65 from both sides:
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{{{5w^2 + 2w - 65 = 0}}}
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Apply the quadratic formula to solve for w. When you do you get:
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{{{w = (-2 +- sqrt( 2^2-4*5*(-65) ))/(2*5) }}}
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The term in the radical simplifies to:
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{{{sqrt(4 - (-1300)) = sqrt(1304) = 36.1109}}} 
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Substituting this for the radical results in:
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{{{w = (-2 +- 36.1109)/(2*5) }}}
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If you let the +- sign be negative you get a negative answer for w. That doesn't make sense
so we just use the + sign to get:
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{{{w = (-2 + 36.1109)/10 = +34.1109/10 = 3.41109}}} and this rounds to 3.41 cm.
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This agrees with your answer, so you are correct.
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