Question
Reynaldo rode his bike 2 miles north and 3 miles east. Which equation should he use to find the distance, d, that takes him directly back home?
A triangle has side lengths 2, 3, and hypotenuse d.
2 squared + 3 squared = d squared
3 squared minus 2 squared = d squared
d squared + 2 squared = 3 squared
d squared + 3 squared = 2 squared
A triangle has side lengths 2, 3, and hypotenuse d.
2 squared + 3 squared = d squared
3 squared minus 2 squared = d squared
d squared + 2 squared = 3 squared
d squared + 3 squared = 2 squared
Answers
GPT-4o mini
To find the distance, \(d\), that takes Reynaldo directly back home after riding 2 miles north and 3 miles east, we can use the Pythagorean theorem. The path he took creates a right triangle where:
- One leg of the triangle represents the distance traveled north (2 miles).
- The other leg represents the distance traveled east (3 miles).
- The hypotenuse \(d\) represents the direct distance back home.
According to the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
where \(a\) and \(b\) are the lengths of the legs of the triangle and \(c\) is the length of the hypotenuse. In this case, we set:
- \(a = 2\) (north)
- \(b = 3\) (east)
- \(c = d\)
Thus, the equation will be:
\[
2^2 + 3^2 = d^2
\]
So the correct equation Reynaldo should use to find the distance \(d\) back home is:
**2 squared + 3 squared = d squared**.
- One leg of the triangle represents the distance traveled north (2 miles).
- The other leg represents the distance traveled east (3 miles).
- The hypotenuse \(d\) represents the direct distance back home.
According to the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
where \(a\) and \(b\) are the lengths of the legs of the triangle and \(c\) is the length of the hypotenuse. In this case, we set:
- \(a = 2\) (north)
- \(b = 3\) (east)
- \(c = d\)
Thus, the equation will be:
\[
2^2 + 3^2 = d^2
\]
So the correct equation Reynaldo should use to find the distance \(d\) back home is:
**2 squared + 3 squared = d squared**.