the side length of the 3 squares are consecutive integers . what the total area
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The 3 consecutive integers are
n
n + 1
n + 2
Then
n2 + (n + 1)2 + (n + 2)2 = 194
n2 + (n2 + 2n + 1) + (n2 + 4n + 4) = 194
3n2 + 6n + 5 = 194
3n2 + 6n - 189 = 0
n2 + 2n - 63 = 0
(n - 7)(n + 9) = 0
n = 7 or -9
If n = 7, the 3 integers are 7, 8, and 9
If n = -9, the 3 integers are -9, -8, and -7
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The 3 consecutive integers are
n
n + 1
n + 2
Then
n2 + (n + 1)2 + (n + 2)2 = 194
n2 + (n2 + 2n + 1) + (n2 + 4n + 4) = 194
3n2 + 6n + 5 = 194
3n2 + 6n - 189 = 0
n2 + 2n - 63 = 0
(n - 7)(n + 9) = 0
n = 7 or -9
If n = 7, the 3 integers are 7, 8, and 9
If n = -9, the 3 integers are -9, -8, and -7
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