SOLUTION: The side of one square is one inch longer than twice the length of the side of a aecond square. The difference of the areas of the square is 96inē. Find the length of a side of ea

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Question 886368: The side of one square is one inch longer than twice the length of the side of a aecond square.
The difference of the areas of the square is 96inē. Find the length of a side of each square.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = side of square 1
2x+1 = side of square 2

difference in the areas is equal to 96 square inches.

that would be area of square 2 minus area of square 1 = 96

area of square 1 = x^2
area of square 2 = (2x+1)^2 = 4x^2 + 4x + 1

you get:

4x^2 + 4x + 1 - x^2 = 96

simplify to get:

3x^2 + 4x - 95 = 0

factor this to get:

(x-5) * (3x+19) = 0

solve for x to get:

x = 5 or x = -19/3

x can't be negative, so your solution can only be x = 5

replace x with 5 in the original equation to see if it holds true.

your original equation is:

x^2 = area of square 1
(2x+1)^2 = area of square 2
square 2 - square 1 = 96

replacing x with 5, we get:
area of square 1 = 25
area of square 2 = 121
square 2 - square 1 area = 121 - 25 = 96

x = 5 is your answer.