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
42.7m
42.7m
912.5 m
912.5 m
8 m
8 m
15 m
Responses
42.7m
42.7m
912.5 m
912.5 m
8 m
8 m
15 m
Answers
GPT-4o mini
To determine how far Jimmy could have jogged in a straight line from his starting point to his final position, we can use the Pythagorean theorem.
Here's the breakdown of his movements:
1. He ran 40 meters west.
2. Then he turned and ran 15 meters north.
This forms a right triangle where:
- One leg of the triangle is 40 meters (the westward leg).
- The other leg of the triangle is 15 meters (the northward leg).
To find the straight-line distance (hypotenuse) \(d\), we can use the formula:
\[
d = \sqrt{(40^2) + (15^2)}
\]
Calculating this:
\[
d = \sqrt{(1600) + (225)} = \sqrt{1825}
\]
Calculating \(\sqrt{1825}\):
\[
\sqrt{1825} \approx 42.72
\]
So, the straight-line distance Jimmy could have jogged is approximately 42.7 meters.
Therefore, the answer is **42.7 m**.
Here's the breakdown of his movements:
1. He ran 40 meters west.
2. Then he turned and ran 15 meters north.
This forms a right triangle where:
- One leg of the triangle is 40 meters (the westward leg).
- The other leg of the triangle is 15 meters (the northward leg).
To find the straight-line distance (hypotenuse) \(d\), we can use the formula:
\[
d = \sqrt{(40^2) + (15^2)}
\]
Calculating this:
\[
d = \sqrt{(1600) + (225)} = \sqrt{1825}
\]
Calculating \(\sqrt{1825}\):
\[
\sqrt{1825} \approx 42.72
\]
So, the straight-line distance Jimmy could have jogged is approximately 42.7 meters.
Therefore, the answer is **42.7 m**.