How long a rope is required to reach from the top of a building 40 ft. high to the ground 30 ft. from the base of the building?

To find the length of the rope required, we can use the Pythagorean theorem. The height of the building is one leg of the right triangle (40 ft), and the distance from the base of the building to the point on the ground is the other leg (30 ft). The length of the rope is the hypotenuse:

[ \text{Length} = \sqrt{(40^2 + 30^2)} = \sqrt{1600 + 900} = \sqrt{2500} = 50 \text{ ft}. ]

Thus, a rope of 50 feet is required.