A ladder is placed against a wall so that it reaches 24 feet up the wall. The base is 10 feet from the wall. How long is the ladder?
Pythagorean Theorem
a^2 + b^2 = L^2
24^2 + 10^2 = L^2
To determine the length of the ladder, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the wall, the floor, and the ladder form a right triangle. The wall represents the height, the floor represents the base, and the ladder represents the hypotenuse.
Using the Pythagorean Theorem, we can calculate the length of the ladder:
Ladder^2 = Height^2 + Base^2
Let's substitute the given values into the equation:
Ladder^2 = 24^2 + 10^2
Simplifying this equation:
Ladder^2 = 576 + 100
Ladder^2 = 676
Taking the square root of both sides to solve for the ladder:
Ladder = √676
Ladder = 26 feet
Therefore, the length of the ladder is 26 feet.