SOLUTION: One of the important cities of the ancient world was Babylon. Greek historians wrote that the city was square-shaped. Its area numerically exceeded its perimeter by about 124. Find

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Question 155899: One of the important cities of the ancient world was Babylon. Greek historians wrote that the city was square-shaped. Its area numerically exceeded its perimeter by about 124. Find its dimensions in miles. Round to the nearest tenth.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
One of the important cities of the ancient world was Babylon. Greek historians wrote that the city was square-shaped. Its area numerically exceeded its perimeter by about 124. Find its dimensions in miles. Round to the nearest tenth.
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If it's a square with sides of length L,
Area = L*L
S = 4L (S = perimeter)
L*L = 4L + 124
L^2 - 4L - 124 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B-124+=+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=%28-4%29%5E2-4%2A1%2A-124=512.

Discriminant d=512 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+512+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+512+%29%29%2F2%5C1+=+13.3137084989848
x%5B2%5D+=+%28-%28-4%29-sqrt%28+512+%29%29%2F2%5C1+=+-9.31370849898476

Quadratic expression 1x%5E2%2B-4x%2B-124 can be factored:
1x%5E2%2B-4x%2B-124+=+%28x-13.3137084989848%29%2A%28x--9.31370849898476%29
Again, the answer is: 13.3137084989848, -9.31370849898476. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-124+%29

The on site solver always uses x.
L = 13.3 (ignore the negative number)
So the perimeter s = 53.2
Area = 176.9, which is apx 124 more.