Joan holds a $26$-inch long piece of light-weight string with a heavy bead on it. One end is in her right hand; the other is in her left hand. Initially, her hands are together. How many inches apart must she pull her hands, keeping them at the same height, so the bead moves upward by $8$ inches?
Source: NCTM Mathematics Teacher 2006

SOLUTION

By the Pythagorean theorem
$5^2+x^2=13^2$
$x^2=13^2-5^2$
$x=\pm\sqrt{144}$
$=\pm 12$
Her hands are apart by $2\times 12=24$ inches.

Answer: $24$ inches