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)Responses2.8 miles2.8 miles0 miles0 miles5.2 miles5.2 miles1.2 miles1.2 miles

Answer 1

To determine how much distance Keith would have saved by riding directly to the grocery store instead of following the two turns, we can use the Pythagorean theorem.

He rode 2 miles down one road and then took a 90-degree turn and rode another 2 miles down a different road. This forms a right triangle where the two legs are 2 miles each.

Using the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]
where \(a\) and \(b\) are the lengths of the two legs of the triangle (both 2 miles).

Calculating:
\[
c = \sqrt{2^2 + 2^2} = \sqrt{4 + 4} = \sqrt{8} \approx 2.83 \text{ miles}
\]

Now, the total distance Keith rode following the two paths is:
\[
2 \text{ miles} + 2 \text{ miles} = 4 \text{ miles}
\]

To find out how much distance he would have saved, we subtract the direct distance from the total distance he rode:
\[
\text{Distance saved} = 4 \text{ miles} - 2.83 \text{ miles} \approx 1.17 \text{ miles}
\]
Rounding to the nearest tenth:
\[
\text{Distance saved} \approx 1.2 \text{ miles}
\]

Thus, the answer is **1.2 miles**.