To determine the distance Keith would have saved by riding directly to the grocery store, we need to calculate the straight-line distance between his starting point and the store using the Pythagorean theorem.
Keith rode 2 miles down one road and then took a 90-degree turn and rode another 2 miles down a different road. This situation forms a right triangle, where each leg of the triangle is 2 miles.
Using the Pythagorean theorem:
\[ c = \sqrt{a^2 + b^2} \]
where:
- \( a = 2 \) miles (distance down the first road)
- \( b = 2 \) miles (distance down the second road)
- \( c \) is the straight-line distance from his house to the grocery store.
Now calculating:
\[ c = \sqrt{2^2 + 2^2} \] \[ c = \sqrt{4 + 4} \] \[ c = \sqrt{8} \] \[ c = 2\sqrt{2} \]
Now, calculating \( 2\sqrt{2} \):
Approximating \( \sqrt{2} \) (which is approximately 1.414):
\[ c \approx 2 \times 1.414 \approx 2.828 \text{ miles} \]
Now, to find the distance Keith rode compared to the direct distance:
Distance rode to the store = \( 2 + 2 = 4 \text{ miles} \)
Distance saved = Distance rode - Direct distance = \( 4 - 2.828 \approx 1.172 \text{ miles} \)
Rounding to the nearest tenth:
The distance saved by riding directly is approximately 1.2 miles.
So the answer is:
1.2 miles.
1 answer