SOLUTION: A piece of wire 20 ft long into two pieces so that the sum of the squares of the length of each piece is 202 square feet. Find the length of each piece.

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Question 665249: A piece of wire 20 ft long into two pieces so that the sum of the squares of the length of each piece is 202 square feet. Find the length of each piece.
Answer by ankor@dixie-net.com(22740) (Show Source):
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A piece of wire 20 ft long into two pieces so that the sum of the squares of the length of each piece is 202 square feet. Find the length of each piece.
:
Let x and y be the two pieces of wire
then
x + y = 20
y = (20-x)
:
x^2 + y^2 = 202
:
Replace y with (20-x)
x^2 + (20-x)^2 = 202
:
FOIL (20-x)(20-x)
x^2 + 400 - 20x - 20x + x^2 = 202
:
Combine like terms on the left, to form a quadratic equation
2x^2 - 40x + 400 - 202 = 0
2x^2 - 40x + 198
:
simplify, divide by 2
x^2 - 20x + 99 = 0
:
Factors to
(x-11)(x-9) = 0
two solutions
x = 11 ft, then y = 9
or
x = 9 ft< then y = 11
:
:
Check this
11^2 + 9^2 =
121 + 81 = 202