Question

Jimmy ran 20 meters west from home and then turned north to jog 25 meters. Jimmy ran 45 meters, but could have arrived at the same point by jogging in a straight line. (3 points)
Put responses in the correct input to answer the question.
Drawing a straight line from the starting point to the ending point would create a Response area triangle.

You can use the Response area to find the direct straight line distance for Jimmy.

If Jimmy took the direct line, he would have traveled approximately Response area meters.

Answer 1

To determine Jimmy's direct straight line distance from his starting point to his ending point, we can visualize his movement as forming a right triangle where:

- He runs 20 meters west (let's call this the horizontal leg of the triangle).
- Then he runs 25 meters north (let's call this the vertical leg of the triangle).

To find the direct distance (the hypotenuse of the triangle), we can use the Pythagorean theorem, which states:

\[
c = \sqrt{a^2 + b^2}
\]

where \( c \) is the hypotenuse, and \( a \) and \( b \) are the other two sides.

Here, \( a = 20 \) meters and \( b = 25 \) meters.

Now, we calculate:

\[
c = \sqrt{20^2 + 25^2} = \sqrt{400 + 625} = \sqrt{1025}
\]

Now, we can simplify \( \sqrt{1025} \):

\[
\sqrt{1025} \approx 32.0157 \text{ meters}
\]

So we can round it to approximately 32 meters.

Now we can fill in the responses:

- Drawing a straight line from the starting point to the ending point would create a **right triangle**.
- If Jimmy took the direct line, he would have traveled approximately **32** meters.