A tower is broken at a height of 12m from the floor and its top touches the floor at a distance of 5 m from the base of the tower. Find the actual height of the tower.

Options

A. 20m
B. 36m
C. 18m
D. 25m

Answer

To find the actual height of the tower, we can use the Pythagorean theorem. Let's break down the solution step by step:

### Step 1: Understand the problem
We have a tower that is broken at a height of 12 meters from the floor. The top of the tower touches the ground at a distance of 5 meters from the base of the tower. We need to find the total height of the tower before it was broken.

### Step 2: Define the variables
- Let the total height of the tower be \( h \).
- The height of the broken part (from the floor to the break) is 12 meters.
- The distance from the base of the tower to the point where the top touches the ground is 5 meters.

### Step 3: Visualize the situation
When the tower breaks, it forms a right triangle:
- One leg of the triangle is the height of the broken part (12 meters).
- The other leg is the distance from the base of the tower to the point where the top touches the ground (5 meters).
- The hypotenuse is the remaining part of the tower, which is the height from the break to the top of the tower.

### Step 4: Apply the Pythagorean theorem
According to the Pythagorean theorem, we have:
\[ \text{(height of the broken part)}^2 + \text{(distance from base)}^2 = \text{(total height of the tower)}^2 \]
Substituting the known values:
\[ 12^2 + 5^2 = h^2 \]
Calculating the squares:
\[ 144 + 25 = h^2 \]
\[ 169 = h^2 \]

### Step 5: Solve for \( h \)
To find \( h \), we take the square root of both sides:
\[ h = \sqrt{169} \]
\[ h = 13 \text{ meters} \]

### Step 6: Find the actual height of the tower
The actual height of the tower is the height of the broken part plus the height from the break to the top:
\[ \text{Actual height} = \text{height of the broken part} + \text{height from break to top} \]
Since the height from the break to the top is also \( h - 12 \) (where \( h \) is the total height):
\[ \text{Actual height} = 12 + (h - 12) = 13 \text{ meters} \]

Thus, the actual height of the tower is **13 meters**.