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

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) (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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=512 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 13.3137084989848, -9.31370849898476. Here's your graph:

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.

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