Question 404117
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)
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given:
(1) {{{4a + 4b = 8}}} in
(2) {{{a^2 + b^2 = 2}}} in2
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from (1):
{{{a + b = 2}}}
Square both sides
{{{a^2 + 2ab + b^2 = 4}}}
{{{a^2 + b^2 = 4 - 2ab}}}
Substitute this in (2):
{{{4 - 2ab = 2}}}
{{{2ab = 2}}}
{{{ab = 1}}}
{{{b = 1/a}}}
and, substituting in (1):
{{{a + 1/a = 2}}}
{{{a^2 + 1 = 2a}}}
{{{a^2 - 2a + 1 = 0}}}
{{{(a - 1)^2 = 0}}}
{{{a = 1}}}
{{{b = 1}}}