Final answer:
Using the Pythagorean theorem, the length of the ladder required to reach a window 12 feet above the ground, with the base 5 feet away from the building, is found to be 13 feet.
Step-by-step explanation:
To determine the length of the ladder needed to reach the window that is 12 feet above the ground, we can use the Pythagorean theorem, which applies to right-angled triangles. The problem describes a right-angled triangle with the window as the vertical side (perpendicular to the ground), the ladder as the hypotenuse (longest side of the triangle), and the distance from the building to the bottom of the ladder as the horizontal side (base of the triangle).
We are given that the height of the window (vertical side) is 12 feet, and the distance from the bottom of the ladder to the building (horizontal base) is 5 feet. Appyling the Pythagorean theorem (a2 + b2 = c2), we can solve for the hypotenuse c:
- Vertical side (a): 12 feet
- Horizontal side (b): 5 feet
- Hypotenuse (c): Unknown
Calculation:
a2 + b2 = c2
122 + 52 = c2
144 + 25 = c2
169 = c2
c = √169
c = 13 feet
Therefore, the length of the ladder is 13 feet, which corresponds to option D.