A rectangular frame with side lengths 30 and 40 units is hung on a wall with nails at four corners as shown in Figure 1, with side AB parallel to the ground and at height $h$ units from the ground. Then, except for the nail at corner A, the other nails loosen and fall, and the frame rotating around corner A comes to rest as shown in Figure 2 with all corners touching the wall when corner C touches the ground. If the heights of corners B and D from the ground are equal in this equilibrium position, what is $h$ in units? A) 42 B) 48 C) 54 D) 60 E) 64
A rectangular frame with side lengths 30 and 40 units is hung on a wall with nails at four corners as shown in Figure 1, with side AB parallel to the ground and at height $h$ units from the ground. Then, except for the nail at corner A, the other nails loosen and fall, and the frame rotating around corner A comes to rest as shown in Figure 2 with all corners touching the wall when corner C touches the ground.
If the heights of corners B and D from the ground are equal in this equilibrium position, what is $h$ in units?\\
A) 42\\
B) 48\\
C) 54\\
D) 60\\
E) 64