Final answer:
To determine the length of the ladder, apply the Pythagorean theorem to the right triangle with sides of 5.5 feet and 12.75 feet to find the hypotenuse, which calculates to approximately 13.88 feet.
Step-by-step explanation:
To find the length of the ladder, we can use the Pythagorean theorem because we are dealing with a right triangle, where the ladder serves as the hypotenuse, the distance from the base of the house to the bottom of the ladder is one leg, and the height the ladder reaches up the side of the house is the other leg.
Given that the distance from the base of the house to the bottom of the ladder is 5 1/2 feet (5.5 feet) and the height the ladder reaches up the side of the house is 12 3/4 feet (12.75 feet), we can set up our equation:
5.52 + 12.752 = x2
After calculating:
x2 = 30.25 + 162.5625 = 192.8125
Then take the square root to find the ladder length:
x = √192.8125 ≈ 13.88 feet
Therefore, the length of the ladder is closest to 13.88 feet.