SOLUTION: Good evening tutor can you tell me if I have this problem correct? THe length of the retangle is 2 cm more than 5 times its width. If the area of the rectangle is 65 cm^2, fin

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Question 105084: Good evening tutor can you tell me if I have this problem correct?
THe length of the retangle is 2 cm more than 5 times its width. If the area of the rectangle is 65 cm^2, find the width of the rectangle to the nearest hundredth.
Could you tell me if the answer is 3.41 cm? Thanks for your help.
Found 2 solutions by bucky, Earlsdon:
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Your answer is correct.
.
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%5E2+%2B+2w+=+65
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Subtract 65 from both sides:
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5w%5E2+%2B+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+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A5%2A%28-65%29+%29%29%2F%282%2A5%29+
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The term in the radical simplifies to:
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sqrt%284+-+%28-1300%29%29+=+sqrt%281304%29+=+36.1109
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Substituting this for the radical results in:
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w+=+%28-2+%2B-+36.1109%29%2F%282%2A5%29+
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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+=+%28-2+%2B+36.1109%29%2F10+=+%2B34.1109%2F10+=+3.41109 and this rounds to 3.41 cm.
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This agrees with your answer, so you are correct.
.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let L = the length and W = the width.
From the problem description, you can write:
L = 5W+2 "The length (L) of the rectangle is (=) 2 more (+2) than 5 times its width (5W)"
A = 65 sq.cm. "The area of the rectangle is 65 sq.cm."
The formula for the area of a rectangle is:
A = L*W Make the appropriate substitutions.
65+=+%285W%2B2%29%2AW Simplify and solve for W.
65+=+5W%5E2+%2B+2W Subtract 65 from both sides.
5W%5E2%2B2W-65+=+0 Use the quadratic formula to solve for W.
W+=+%28-2%2B-sqrt%282%5E2-4%285%29%28-65%29%29%29%2F2%285%29
W+=+-3.811 Discard the negative solution.
W+=+3.411
The width is 3.41 cm