Finding the Length of a Ladder Using the Pythagorean Theorem

Based on the image provided, the problem states:
“A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 4 feet less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 6 feet.”

Step 1: Define the variables.
Let be the length of the ladder (the hypotenuse of the right triangle).
The distance from the ground to the top of the ladder (the height) is .
The distance from the bottom of the ladder to the building (the base) is .

Step 2: Apply the Pythagorean theorem.
According to the Pythagorean theorem, :

Step 3: Solve for .
Expand the squared term and simplify:

Subtract from both sides:

The length of the ladder is feet.

Final Answer:
The length of the ladder is feet.