SOLUTION: A piece of wire is 8 inches long. The wire is cut into two pieces and then each piece is bent into s square. Find the length of each piece if the sum of the areas of these squares

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Question 404117: A piece of wire is 8 inches long. The wire is cut into two pieces and then each piece is bent into s square. Find the length of each piece if the sum of the areas of these squares is to be 2 square inches.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The wire is cut into
(a) 4 lengths all the same length
(b) 4 more lengths all the same length
Let a = length in inches of each length in (a)
Let b = length in inches of each length in (b)
-------------
given:
(1) 4a+%2B+4b+=+8 in
(2) a%5E2+%2B+b%5E2+=+2 in2
---------------------
from (1):
a+%2B+b+=+2
Square both sides
a%5E2+%2B+2ab+%2B+b%5E2+=+4
a%5E2+%2B+b%5E2+=+4+-+2ab
Substitute this in (2):
4+-+2ab+=+2
2ab+=+2
ab+=+1
b+=+1%2Fa
and, substituting in (1):
a+%2B+1%2Fa+=+2
a%5E2+%2B+1+=+2a
a%5E2+-+2a+%2B+1+=+0
%28a+-+1%29%5E2+=+0
a+=+1
b+=+1