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.

Answer 1

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

Keith rode 2 miles down one road and then took a 90-degree turn to ride another 2 miles down a different road. This forms a right triangle, where:

- One leg of the triangle (a) = 2 miles
- The other leg of the triangle (b) = 2 miles

Using the Pythagorean theorem:

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

Substituting in the values of \(a\) and \(b\):

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

Calculating \(2\sqrt{2}\):

\[
2\sqrt{2} \approx 2 \times 1.414 \approx 2.828
\]

Now, this is the distance Keith would have traveled directly to the grocery store.

The distance he actually rode is:

\[
2 \text{ miles} + 2 \text{ miles} = 4 \text{ miles}
\]

To find out how much distance he saved by taking a direct route, we subtract the direct distance \(c\) from the actual distance he rode:

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

Rounding this to the nearest tenth gives:

\[
\text{Distance saved} \approx 1.2 \text{ miles}
\]

Thus, the distance Keith would have saved is approximately **1.2 miles**.