SOLUTION: The perimeter of one square exceeds that of another by 16 and its area is 44 less than the 4 times the area of the other. What is the length of the side of each square?

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Question 165936: The perimeter of one square exceeds that of another by 16 and its area is 44 less than the 4 times the area of the other. What is the length of the side of each square?

Answer by nerdybill(7384) (Show Source):
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The perimeter of one square exceeds that of another by 16 and its area is 44 less than the 4 times the area of the other. What is the length of the side of each square?
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Perimeter of any square equals 4 times the length of a side.
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Let x = length of a side of smaller square
and y = length of a side of larger square
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From:"The perimeter of one square exceeds that of another by 16"
4x = 4y+16
dividing through by 4:
x = y + 4 (equation 1)
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From:"its area is 44 less than the 4 times the area of the other"
x^2 = 4y^2 - 44 (equation 2)
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Substitute the value of 'x' from equation 1 into equation 2 and solve for y:
x^2 = 4y^2 - 44
(y + 4)^2 = 4y^2 - 44
y^2 + 8y + 16 = 4y^2 - 44
8y + 16 = 3y^2 - 44
16 = 3y^2 - 8y - 44
0 = 3y^2 - 8y - 60
Solving using the quadratic equation will yield:
x = {6, -3.33333333333333}
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We can toss out the negative answer leaving:
x = 6
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To find y, substitute x into equation 1 and solve:
x = y + 4
6 = y + 4
2 = y
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Solution: 6 and 2
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Below is the details of the quadratic solution:
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Solved by pluggable solver: SOLVE quadratic equation with variable

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=784 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6, -3.33333333333333. Here's your graph: