Question
Mara ran 3 km north and then 4 km east. She will finish her run by running directly home. What was the total distance of her run?
A right triangle with side lengths 8 kilometers and 4 kilometers. A point at intersection of the side with length 3 kilometers and the hypotenuse is labeled Mara's House.
5 km
7 km
12 km
14 km
A right triangle with side lengths 8 kilometers and 4 kilometers. A point at intersection of the side with length 3 kilometers and the hypotenuse is labeled Mara's House.
5 km
7 km
12 km
14 km
Answers
GPT-4o mini
To determine the total distance of Mara's run, we can break it down into the segments she ran and then find the straight-line distance back to her starting point (home).
1. **Segment 1**: Mara runs 3 km north.
2. **Segment 2**: She then runs 4 km east.
Now, we can visualize these two segments as forming a right triangle where:
- One leg is 3 km (north).
- The other leg is 4 km (east).
To find the distance directly back home (the hypotenuse of the triangle), we can use the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]
where:
- \( a = 3 \) km (north),
- \( b = 4 \) km (east).
Calculating this:
\[
c = \sqrt{(3^2) + (4^2)} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ km}
\]
Now, Mara's total distance run can be calculated by summing the distances of the three legs of her journey:
- First segment: 3 km north
- Second segment: 4 km east
- Third segment: 5 km back home
Total distance:
\[
3 \text{ km} + 4 \text{ km} + 5 \text{ km} = 12 \text{ km}
\]
Thus, the total distance of Mara's run is **12 km**.
1. **Segment 1**: Mara runs 3 km north.
2. **Segment 2**: She then runs 4 km east.
Now, we can visualize these two segments as forming a right triangle where:
- One leg is 3 km (north).
- The other leg is 4 km (east).
To find the distance directly back home (the hypotenuse of the triangle), we can use the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]
where:
- \( a = 3 \) km (north),
- \( b = 4 \) km (east).
Calculating this:
\[
c = \sqrt{(3^2) + (4^2)} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ km}
\]
Now, Mara's total distance run can be calculated by summing the distances of the three legs of her journey:
- First segment: 3 km north
- Second segment: 4 km east
- Third segment: 5 km back home
Total distance:
\[
3 \text{ km} + 4 \text{ km} + 5 \text{ km} = 12 \text{ km}
\]
Thus, the total distance of Mara's run is **12 km**.