Answer
The lengths are 24 and 32 inches.
Work Step by Step
We will call the length of the first wire x and the length of the second wire y. Thus, we find:
$ 56 = x+y$
And:
$(.25x)^2 + (.25y)^2 = 100 \\ 1/16 (x^2 + y ^2) = 100 \\ x^2 + y^2 = 1600$
Plugging in y = 56 - x, we find:
$ x^2 + (56 -x)^2 = 1600 \\ 2x^2 - 112x +1536 = 0 \\ 2(x-32)(x-24)$
Thus, we find that the lengths are 32 and 24 inches.
