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

Options

A. 11 km
B. 18 km
C. 15 km
D. 13 km

Answer

To find the straight-line distance of the ship from its starting point after sailing, we can use the Pythagorean theorem. Here’s a step-by-step solution:

### Step 1: Understand the Movement of the Ship
The ship first sails 12 km south and then 5 km east. We can visualize this movement as forming a right triangle where:
- One leg (AB) is the distance sailed south (12 km).
- The other leg (BC) is the distance sailed east (5 km).

### Step 2: Identify the Triangle
Let:
- Point A be the starting point of the ship.
- Point B be the point after sailing south (12 km).
- Point C be the final position of the ship after sailing east (5 km).

We need to find the distance AC, which is the hypotenuse of the right triangle ABC.

### Step 3: Apply the Pythagorean Theorem
According to the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]

Substituting the known values:
- \( AB = 12 \) km
- \( BC = 5 \) km

We get:
\[ AC^2 = (12)^2 + (5)^2 \]
\[ AC^2 = 144 + 25 \]
\[ AC^2 = 169 \]

### Step 4: Calculate the Distance AC
To find AC, we take the square root of both sides:
\[ AC = \sqrt{169} \]
\[ AC = 13 \text{ km} \]

### Conclusion
The straight-line distance of the ship from the starting point is **13 km**.

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