Question

A 25 ft long ladder is placed against the wall with its base 7 ft from the wall. The base of the ladder is drawn out so that the top comes down by half the distance that the base is drawn out. This distance is in the range:

Accepted Answer

E. 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.

Geometry: Ladder Sliding

Explanation

Practise this under exam conditions