SOLUTION: A concrete border of uniform width is constructed around a rectangular flower bed that is 12ft by 9 ft. Find the width of the border if the area formed by the flower bed and the bo

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Question 242913: A concrete border of uniform width is constructed around a rectangular flower bed that is 12ft by 9 ft. Find the width of the border if the area formed by the flower bed and the border is 154 sq ft.
Can you help me solve this word problem.
Found 2 solutions by checkley77, JimboP1977:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(12+2x)(9+2x)=154
108+18x+24x+4x^2=154
4x^2+42x+108-154=0
4x^2+42x-46=0
(4x-4)(x+11.5)=0
4x-4=0
4x=4
x=4/4
x=1 ft. ans. for the width of the border.
Proof:
(12+2)(9+2)=154
14*11=154
154=154

Answer by JimboP1977(311) About Me  (Show Source):
You can put this solution on YOUR website!
Best thing to do with problems like this is to draw a diagram.
From the diagram you will see that the area between the border and the flower bed is equal to the 12 foot of the flower bed added to twice the width of the border multiplied by 9 plus twice the width of the bed.
Using Algebra, if x is the unknown width:
%2812%2B2x%29%289%2B2x%29+=+154
4x%5E2%2B24x%2B18x%2B108%29+=+154Multiply out
4x%5E2%2B42x%2B108%29+=+154Collect terms
4x%5E2%2B42x-46%29+=+0Set to zero
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B42x%2B-46+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2842%29%5E2-4%2A4%2A-46=2500.

Discriminant d=2500 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-42%2B-sqrt%28+2500+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2842%29%2Bsqrt%28+2500+%29%29%2F2%5C4+=+1
x%5B2%5D+=+%28-%2842%29-sqrt%28+2500+%29%29%2F2%5C4+=+-11.5

Quadratic expression 4x%5E2%2B42x%2B-46 can be factored:
4x%5E2%2B42x%2B-46+=+4%28x-1%29%2A%28x--11.5%29
Again, the answer is: 1, -11.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B42%2Ax%2B-46+%29


So x must be positive so x is 1 ft