Question

A ladder with a length of 12 feet is leaning against a wall, with the ladder's base 2 feet from the wall. how far up the wall does the ladder reach?

a. 14 feet
b. 12 feet
c. 11.8 feet
d. 4.5 feet

Answer 1

Using the Pythagorean theorem, the ladder reaches approximately 11.8 feet up the wall, making the correct answer option c. 11.8 feet.

Step-by-step explanation:

The problem describes a classic scenario that can be solved using the Pythagorean theorem, which relates the lengths of the sides of a right triangle. The ladder forms the hypotenuse, the distance from the wall to the base of the ladder is one leg, and the distance up the wall to where the ladder touches is the other leg. Here's how we calculate the distance up the wall the ladder reaches:

1. Let x be the distance up the wall where the ladder reaches.
2. We know the ladder length (12 feet, the hypotenuse) and the distance from the base to the wall (2 feet, one of the legs).
3. Apply the Pythagorean theorem:
4. a^2 + b^2 = c^2
5. Substitute the known values: 2^2 + x^2 = 12^2
6. Solve for x: 4 + x^2 = 144
7. Subtract 4 from both sides: x^2 = 140
8. Take the square root of both sides to find x: x ≈ 11.8 feet

The correct option is c. 11.8 feet.