A ladder reaches a window which is 15 metres above the ground on one side of the street. Keeping its food at the same point, the ladder is turned to the other side of the street to reach a window 8 metre high. Find the width of the street, if the length of the ladder is 17 metres.

Answer

To solve the problem step by step, we will use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

### Step 1: Understand the Problem
We have a ladder of length 17 meters that reaches two different heights on either side of the street: 15 meters on one side and 8 meters on the other side. We need to find the width of the street, which is the sum of the horizontal distances from the base of the ladder to the foot of the wall on each side.

### Step 2: Set Up the Diagram
Let's denote:
- Point A: the top of the ladder when it reaches the 15-meter window.
- Point B: the foot of the ladder.
- Point C: the top of the ladder when it reaches the 8-meter window.
- Point D: the foot of the wall on the side with the 8-meter window.
- Let x be the horizontal distance from B to the wall with the 15-meter window.
- Let y be the horizontal distance from B to the wall with the 8-meter window.

### Step 3: Apply the Pythagorean Theorem for the First Triangle
For the triangle formed by the ladder reaching the 15-meter window:
- Hypotenuse (AB) = 17 meters
- Vertical side (height) = 15 meters
- Horizontal side (x) = ?

Using the Pythagorean theorem:
\[ AB^2 = x^2 + (height)^2 \]
\[ 17^2 = x^2 + 15^2 \]
\[ 289 = x^2 + 225 \]

### Step 4: Solve for x
Rearranging the equation:
\[ x^2 = 289 - 225 \]
\[ x^2 = 64 \]
Taking the square root:
\[ x = \sqrt{64} = 8 \text{ meters} \]

### Step 5: Apply the Pythagorean Theorem for the Second Triangle
For the triangle formed by the ladder reaching the 8-meter window:
- Hypotenuse (CD) = 17 meters
- Vertical side (height) = 8 meters
- Horizontal side (y) = ?

Using the Pythagorean theorem:
\[ CD^2 = y^2 + (height)^2 \]
\[ 17^2 = y^2 + 8^2 \]
\[ 289 = y^2 + 64 \]

### Step 6: Solve for y
Rearranging the equation:
\[ y^2 = 289 - 64 \]
\[ y^2 = 225 \]
Taking the square root:
\[ y = \sqrt{225} = 15 \text{ meters} \]

### Step 7: Calculate the Width of the Street
The width of the street is the sum of x and y:
\[ \text{Width of the street} = x + y = 8 + 15 = 23 \text{ meters} \]

### Final Answer
The width of the street is **23 meters**.

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