A 30 -Foot Ladder Is Leaning Against a House (See $r = \frac { 2 x } { \sqrt { 900 - x ^ { 2 } } } \mathrm { ft } / \mathrm { sec }$

Multiple Choice

A 30 -foot ladder is leaning against a house (see figure) . If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of $r = \frac { 2 x } { \sqrt { 900 - x ^ { 2 } } } \mathrm { ft } / \mathrm { sec }$ , where $x$ is the distance between the base of the ladder and the house. Find the rate $r$ when $x$ is 18 feet.

A) $r = \frac { 3 } { 2 } \mathrm { ft } / \mathrm { sec }$
B) $r = \frac { 4 } { 3 } \mathrm { ft } / \mathrm { sec }$
C) $r = \frac { 48 } { 5 } \mathrm { ft } / \mathrm { sec }$
D) $r = \frac { 2 } { 3 } \mathrm { ft } / \mathrm { sec }$
E) $r = \frac { 3 } { 4 } \mathrm { ft } / \mathrm { sec }$