Geometry: Ladder Sliding

Initial height $AB = \sqrt{25^2 - 7^2} = 24$ ft. Base drawn out by $2x$, top comes down by $x$. New base $= 7 + 2x$, new height $= 24 - x$. $(24 - x)^2 + (7 + 2x)^2 = 25^2 \implies 576 - 48x + x^2 + 49 + 28x + 4x^2 = 625 \implies 5x^2 - 20x = 0 \implies x = 4$. Base drawn out $= 2x = 8$ ft. Since 8 is not strictly inside any of the open intervals (2,7), (5,8), (9,10), or (3,7), the answer is E.