SOLUTION: this algebra stuff is so confusing to me. I have a word problem that I don't know how to set up and solve. The length of a rectangle is approximately 1.6 times the width. Find

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Question 173354This question is from textbook intro algebra
: this algebra stuff is so confusing to me. I have a word problem that I don't know how to set up and solve.
The length of a rectangle is approximately 1.6 times the width. Find the dimensions of the rectangle is its are is 9000m^2 This question is from textbook intro algebra

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"The length of a rectangle is approximately 1.6 times the width" translates to L=1.6W


Since the area of any rectangle is A=LW and the area is "9000m^2", this means that A=9000


A=LW Start with the second equation


9000=%281.6W%29W Plug in A=9000 and L=1.6W


9000=W%281.6W%29 Rearrange the terms.


9000=1.6W%5E2 Multiply


9000%2F1.6=W%5E2 Divide both sides by 1.6


5625=W%5E2 Divide.


sqrt%285625%29=W Take the square root of both sides. Note: only the positive square root is considered (since a negative width doesn't make sense)


75=W Take the square root of 5625 to get 75


So the first answer is W=75 which means that the width is 75 meters.


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L=1.6W Go back to the first equation


L=1.6%2875%29 Plug in W=75


L=120 Multiply



So the second answer is L=120 which means that the length is 120 meters.


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Answer:


So the solutions are W=75 and L=120 which means that the width is 75 meters and the length is 120 meters.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is approximately 1.6 times the width. Find the dimensions of the rectangle is its are is 9000m^2
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There is no need to be confused.
1st draw the picture of a rectangle
2nd label the width as "x" and the length as "1.6x"
3rd label the inside (area) as 9000m^2
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4th: write the equation for area: A = (length)(width)
5th: substitute what you know for the words
9000 = 1.6x*x
6th solve for "x"
1.6x^2 = 9000
x^2 = 9000/1.6
x^2 = 5625
x = 75 meters (width)
1.6x = 120 meters (length)
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Cheers,
Stan H.