A ladder is leaning against a wall. The foot of the ladder is $6$ meters away from the wall, and the ladder reaches a height of $8$ meters on the wall. What is the length of the ladder?

• A. $10$ meters
• B. $12$ meters
• C. $14$ meters
• D. $9$ meters

Answer: (A)

Verified step by step guidance

1. Identify the right triangle formed by the ladder, the wall, and the ground. The ladder acts as the hypotenuse, the distance from the wall is one leg, and the height the ladder reaches on the wall is the other leg.
2. Label the sides: let the distance from the wall be \(a = 6\) meters, the height on the wall be \(b = 8\) meters, and the length of the ladder (hypotenuse) be \(c\) meters.
3. Recall the Pythagorean theorem for right triangles: \(c^2 = a^2 + b^2\).
4. Substitute the known values into the equation: \(c^2 = 6^2 + 8^2\).
5. Calculate the squares and sum them: \(c^2 = 36 + 64\), then find \(c\) by taking the square root of the sum, i.e., \(c = \sqrt{36 + 64}\).