SOLUTION: A rectangle has a perimeter of 46 meters. The area is 124 meters squared. Find the dimensions...thank you!

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Question 39163: A rectangle has a perimeter of 46 meters. The area is 124 meters squared. Find the dimensions...thank you!
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
2l+%2B+2w+=+46
lw+=+124
Combine:
l+=+%28124%2Fw%29
Plug:
2l+%2B+2w+=+46
2%28124%2Fw%29+%2B+2w+=+46
%28248%2Fw%29+%2B+2w+=+46
248+%2B+2w%5E2+=+46w
2w%5E2+-+46w+%2B+248+=+0
w%5E2+-+23w+%2B+124+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aw%5E2%2Bbw%2Bc=0 (in our case 1w%5E2%2B-23w%2B124+=+0) has the following solutons:

w%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=%28-23%29%5E2-4%2A1%2A124=33.

Discriminant d=33 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--23%2B-sqrt%28+33+%29%29%2F2%5Ca.

w%5B1%5D+=+%28-%28-23%29%2Bsqrt%28+33+%29%29%2F2%5C1+=+14.372281323269
w%5B2%5D+=+%28-%28-23%29-sqrt%28+33+%29%29%2F2%5C1+=+8.62771867673099

Quadratic expression 1w%5E2%2B-23w%2B124 can be factored:
1w%5E2%2B-23w%2B124+=+1%28w-14.372281323269%29%2A%28w-8.62771867673099%29
Again, the answer is: 14.372281323269, 8.62771867673099. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-23%2Ax%2B124+%29

To finish, plug in the answer (width) in the equation to determine length.