A ship after sailing 12 km to wards south from a particular place covered 5 km more towards east. Then the straightway distance of the ship from that place is

Options

A. a) 11 km
B. b) 18 km
C. c) 15 km
D. d) 13 km

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Movement of the Ship
The ship first sails 12 km towards the south and then 5 km towards the east. We can visualize this movement on a coordinate plane where:
- The starting point (origin) is at (0, 0).
- After moving 12 km south, the ship reaches the point (0, -12).
- After moving 5 km east, the ship reaches the point (5, -12).

### Step 2: Identify the Points
Let:
- Point A (starting point) = (0, 0)
- Point B (after moving south) = (0, -12)
- Point C (after moving east) = (5, -12)

### Step 3: Use the Pythagorean Theorem
To find the straight-line distance (AC) from the starting point A to the final point C, we can use the Pythagorean theorem. According to the theorem:
\[ AC^2 = AB^2 + BC^2 \]
Where:
- \( AB \) is the distance moved south (12 km)
- \( BC \) is the distance moved east (5 km)

### Step 4: Calculate the Distances
Now, we can plug in the values:
- \( AB = 12 \) km
- \( BC = 5 \) km

Calculating:
\[ AC^2 = 12^2 + 5^2 \]
\[ AC^2 = 144 + 25 \]
\[ AC^2 = 169 \]

### Step 5: Find the Square Root
Now, take the square root to find AC:
\[ AC = \sqrt{169} \]
\[ AC = 13 \] km

### Final Answer
The straight-line distance of the ship from the starting place is **13 km**.

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