SOLUTION: Could you please help me with figuring out how to do this? The length of a top of a board is 6m greater than width. The area is 72m^2. Find the diminsions for width of board and

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Question 149613: Could you please help me with figuring out how to do this?
The length of a top of a board is 6m greater than width. The area is 72m^2. Find the diminsions for width of board and length of board.
Thank you for any help.
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let L=length and W=width


Since the "length of a top of a board is 6m greater than width", this means that the first equation is L=W%2B6. Also, since the "area is 72m^2", this tells us that A=L%2AW=72 or A=72


A=L%2AW Start with the given equation.


72=%28W%2B6%29%2AW Plug in A=72 and L=W%2B6.


72=W%5E2%2B6W Distribute


0=W%5E2%2B6W-72 Subtract 72 from both sides.


Let's use the quadratic formula to solve for W


W+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


W+=+%28-%286%29+%2B-+sqrt%28+%286%29%5E2-4%281%29%28-72%29+%29%29%2F%282%281%29%29 Plug in a=1, b=6, and c=-72


W+=+%28-6+%2B-+sqrt%28+36-4%281%29%28-72%29+%29%29%2F%282%281%29%29 Square 6 to get 36.


W+=+%28-6+%2B-+sqrt%28+36--288+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-72%29 to get -288


W+=+%28-6+%2B-+sqrt%28+36%2B288+%29%29%2F%282%281%29%29 Rewrite sqrt%2836--288%29 as sqrt%2836%2B288%29


W+=+%28-6+%2B-+sqrt%28+324+%29%29%2F%282%281%29%29 Add 36 to 288 to get 324


W+=+%28-6+%2B-+sqrt%28+324+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


W+=+%28-6+%2B-+18%29%2F%282%29 Take the square root of 324 to get 18.


W+=+%28-6+%2B+18%29%2F%282%29 or W+=+%28-6+-+18%29%2F%282%29 Break up the expression.


W+=+%2812%29%2F%282%29 or W+=++%28-24%29%2F%282%29 Combine like terms.


W+=+6 or W+=+-12 Simplify.


Since a negative width is not possible, the only possible width is W+=+6


So the width is 6 m


L=W%2B6 Go back to the first equation.


L=6%2B6 Plug in W=6


L=12 Add


So the length is 12 m

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!

The length of a top of a board is 6m greater than width. The area is 72m^2. Find the diminsions for width of board and length of board.
------------------
Let width be "x" meters.
Then length is "x+6" meters.
----------------
Area = width*length = 72m^2
x(x+6) = 72
x^2+6x-72 = 0
(x+12)(x-6) = 0
Positive solution:
x = 6 meters (width)
x+6 = 12 meters (length)
===========================
Cheers,
Stan H.