A ladder 5 m long leans against a vertical wall. The bottom of the ladder is 3m from the wall. If the bottom of the ladder is pulled 1 m farther from the wall, how much does the top of the ladder slide down the wall

Options

A. 1 m
B. 4 m
C. 2 m
D. 3 m

Answer

To solve the problem step by step, we will use the Pythagorean theorem.

### Step 1: Understand the initial setup
We have a ladder of length 5 m leaning against a wall. The bottom of the ladder is initially 3 m away from the wall. We need to find out how much the top of the ladder slides down when the bottom is pulled 1 m farther away from the wall.

### Step 2: Set up the initial triangle
Let:
- \( AB \) be the ladder (5 m),
- \( AC \) be the distance from the wall to the bottom of the ladder (3 m),
- \( BC \) be the height of the ladder on the wall.

Using the Pythagorean theorem:
\[ AB^2 = AC^2 + BC^2 \]
Substituting the known values:
\[ 5^2 = 3^2 + BC^2 \]
\[ 25 = 9 + BC^2 \]
\[ BC^2 = 25 - 9 = 16 \]
\[ BC = \sqrt{16} = 4 \text{ m} \]

### Step 3: Set up the new triangle after pulling the ladder
Now, the bottom of the ladder is pulled 1 m farther from the wall, making the new distance \( AC' = 3 + 1 = 4 \) m. We need to find the new height \( BC' \) of the ladder on the wall.

Using the Pythagorean theorem again:
\[ AB^2 = AC'^2 + BC'^2 \]
Substituting the new values:
\[ 5^2 = 4^2 + BC'^2 \]
\[ 25 = 16 + BC'^2 \]
\[ BC'^2 = 25 - 16 = 9 \]
\[ BC' = \sqrt{9} = 3 \text{ m} \]

### Step 4: Calculate how much the top of the ladder slides down
The initial height of the ladder on the wall was \( BC = 4 \) m, and after pulling the ladder, the new height is \( BC' = 3 \) m.

The amount the top of the ladder slides down is:
\[ \text{Slide down} = BC - BC' = 4 - 3 = 1 \text{ m} \]

### Final Answer
The top of the ladder slides down the wall by **1 meter**.

---