SOLUTION: a piece of wire 20 ft long is cut into 2 pieces so that the sum of the squares of the length of each piece is 202 . find the length of each piece

Question 822143: a piece of wire 20 ft long is cut into 2 pieces so that the sum of the squares of the length of each piece is 202 . find the length of each piece
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
Set x = length of one piece .
The length of the second piece is 20 - x .
x^2 + ( 20 - x )^2 = 202
x^2 + 400 - 40x + x^2 = 202
2x^2 - 40x + 400 = 202
Subtract 202 from each side.
2x^2 - 40x + 198 = 0
Divide each side by 2
x^2 - 20x + 99 = 0
(x - 9)(x - 11) = 0
So x = 9 or x = 11
And we can see that our requirements
are satisfied when the piece lengths are 9 and 11.

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