Question

Keith left his house for the grocery store to buy items for dinner. He rode his bike 2miles down one road, took a 90-degree turn, and rode another 2 miles down a different road before arriving at the store. If he had ridden directly to the grocery store, how much distance would he have saved? Round your answer to the nearest tenth.



(1 point)
Responses

5.2 miles
5.2 miles

2.8 miles
2.8 miles

0 miles
0 miles

1.2 miles
1.2 miles

Answer 1

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**.