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?

This calls for the Pythagorean Theorem

10^2 + x^2 = 24^2

100 + x^2 = 576

x^2 = 476

x = ?

To find the length of the ladder, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this scenario, the wall, the ground, and the ladder form a right triangle. The height of the wall is given as 24 feet, and the distance of the ladder base from the wall is given as 10 feet. We need to find the length of the ladder, which is the hypotenuse.

Using the Pythagorean theorem, we can write the equation:

(length of ladder)^2 = (height of wall)^2 + (distance of ladder base)^2

Let's plug in the given values:

(length of ladder)^2 = 24^2 + 10^2

Simplifying the equation:

(length of ladder)^2 = 576 + 100
(length of ladder)^2 = 676

Now, we take the square root of both sides to find the length of the ladder:

length of ladder = √676
length of ladder = 26 feet

Therefore, the length of the ladder is 26 feet.