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.

Question

(1 point)
Responses

2.8 miles
2.8 miles

0 miles
0 miles

1.2 miles
1.2 miles

5.2 miles
5.2 miles
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Answer 1

To determine how much distance Keith would have saved had he ridden directly to the grocery store, we can use the Pythagorean theorem.

Keith rode 2 miles down one road and then 2 miles down another road, which would create a right triangle where each leg is 2 miles.

Using the Pythagorean theorem:

\[ c^2 = a^2 + b^2 \]

where \( a \) and \( b \) are the lengths of the two legs (2 miles each), and \( c \) is the diagonal (the direct distance to the grocery store).

So we calculate:

\[ c^2 = 2^2 + 2^2 \] \[ c^2 = 4 + 4 \] \[ c^2 = 8 \] \[ c = \sqrt{8} \approx 2.828 \]

Now, we can calculate how much distance Keith saved:

1. The distance he actually rode was 2 miles + 2 miles = 4 miles.
2. The direct distance to the store is approximately 2.828 miles.

To determine the distance saved:

\[ \text{Distance saved} = \text{actual distance} - \text{direct distance} \] \[ \text{Distance saved} = 4 - 2.828 \approx 1.172 \]

Rounding to the nearest tenth gives us approximately 1.2 miles.

Therefore, the answer is:

1.2 miles