SOLUTION: The length of a rectangle garden is 2 less than 3 times the width. If the area is 341in. find the length, width, and perimeter of the rectangle.

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Question 956294: The length of a rectangle garden is 2 less than 3 times the width. If the area is 341in. find the length, width, and perimeter of the rectangle.
Answer by amarjeeth123(569) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width be x.
Then the length is 3x-2
Area=341=length*width
x(3x-2)=341
3x^2-2x-341=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-2x%2B-341+=+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=%28-2%29%5E2-4%2A3%2A-341=4096.

Discriminant d=4096 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+4096+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+4096+%29%29%2F2%5C3+=+11
x%5B2%5D+=+%28-%28-2%29-sqrt%28+4096+%29%29%2F2%5C3+=+-10.3333333333333

Quadratic expression 3x%5E2%2B-2x%2B-341 can be factored:
3x%5E2%2B-2x%2B-341+=+3%28x-11%29%2A%28x--10.3333333333333%29
Again, the answer is: 11, -10.3333333333333. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-2%2Ax%2B-341+%29

x=11
The width of the rectangle is 11 inches.
The length of the rectangle is 31 inches.
Perimeter=2(11+31)=84 inches.