Question
Jimmy ran 40 meters west from home and then turned north to jog 15 meters. Jimmy ran 55 meters, but could have arrived at the same point by jogging in a straight line. How many meters could he have jogged using a straight line distance?(1 point)
Responses:
8 m
8 m
912.5 m
912.5 m
42.7m
42.7m
15 m
Responses:
8 m
8 m
912.5 m
912.5 m
42.7m
42.7m
15 m
Answers
GPT-4o mini
To find out how many meters Jimmy could have jogged in a straight line to reach the same point, we can visualize his route as a right triangle.
1. Jimmy ran 40 meters west (this is one leg of the triangle).
2. Then he turned north and jogged 15 meters (this is the other leg of the triangle).
We can use the Pythagorean theorem, which states that:
\[
c^2 = a^2 + b^2
\]
where \(c\) is the hypotenuse (the straight-line distance) and \(a\) and \(b\) are the two legs of the triangle.
In this case:
- \(a = 40\) meters (west)
- \(b = 15\) meters (north)
Plugging in the values:
\[
c^2 = 40^2 + 15^2
\]
\[
c^2 = 1600 + 225
\]
\[
c^2 = 1825
\]
\[
c = \sqrt{1825} \approx 42.7 \text{ meters}
\]
So, Jimmy could have jogged approximately 42.7 meters in a straight line to reach the same point.
The correct answer is:
**42.7 m**
1. Jimmy ran 40 meters west (this is one leg of the triangle).
2. Then he turned north and jogged 15 meters (this is the other leg of the triangle).
We can use the Pythagorean theorem, which states that:
\[
c^2 = a^2 + b^2
\]
where \(c\) is the hypotenuse (the straight-line distance) and \(a\) and \(b\) are the two legs of the triangle.
In this case:
- \(a = 40\) meters (west)
- \(b = 15\) meters (north)
Plugging in the values:
\[
c^2 = 40^2 + 15^2
\]
\[
c^2 = 1600 + 225
\]
\[
c^2 = 1825
\]
\[
c = \sqrt{1825} \approx 42.7 \text{ meters}
\]
So, Jimmy could have jogged approximately 42.7 meters in a straight line to reach the same point.
The correct answer is:
**42.7 m**