A ladder leans against a vertical wall. The end of the ladder is 8 m above the ground. When the lower end of the ladder is moved 2 m farther away from the wall, the other end of the ladder rests against the foot of the wall. The length of the ladder is:

Question

Accepted Answer

Let the initial horizontal distance of the ladder's lower end from the wall be $$ x $$. When it is moved 2 m farther, the total horizontal distance becomes $$ x + 2 $$.

Using the Pythagorean theorem:  
$$
8^2 + x^2 = (x + 2)^2
$$

Expand and simplify:  
$$
64 + x^2 = x^2 + 4x + 4
$$  
$$
64 = 4x + 4
$$  
$$
4x = 60 \implies x = 15
$$

The length of the ladder is:  
$$
x + 2 = 15 + 2 = 17 \, 	ext{m}
$$

Thus, the correct answer is **(d) 17 m**.

Answer

Answer

Answer