To solve the problem, we will summarize the movements of the mouse in the kitchen.
The mouse starts at the northwest corner (let's denote this point as A), then it moves to the southwest corner (point B), continues to the southeast corner (point C), and finally returns to the northwest corner (point A).
- The distance from the northwest corner (A) to the southwest corner (B) is 4 meters.
- The distance from the southwest corner (B) to the southeast corner (C) is 3 meters.
- Finally, the distance from the southeast corner (C) back to the northwest corner (A) needs to be calculated.
Since point A is in the northwest corner and point C is in the southeast corner of the rectangle, the return path from C to A is the diagonal of the rectangle formed by the length and width.
To calculate the total distance the mouse travels:
- From A to B: 4 meters
- From B to C: 3 meters
- From C back to A: The diagonal formed by 4 meters (length) and 3 meters (width) can be calculated using the Pythagorean theorem.
The diagonal distance \( d \) is given by:
\[ d = \sqrt{(length^2) + (width^2)} = \sqrt{(4^2) + (3^2)} = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ meters} \]
Now, we can find the total scurried distance:
\[ \text{Total distance} = \text{Distance from A to B} + \text{Distance from B to C} + \text{Distance from C to A} \]
\[ \text{Total distance} = 4 + 3 + 5 = 12 \text{ meters} \]
Thus, the total distance the mouse scurries is 12 meters.
5 answers