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 0 miles 0 miles 1.2 miles 1.2 miles 5.2 miles 5.2 miles 2.8 miles 2.8 miles Skip to navigation

Answer 1

To find out how much distance Keith would have saved by riding directly to the grocery store instead of taking two 2-mile segments at a right angle, we can use the Pythagorean theorem.

Keith rode:

• 2 miles down one road
• 2 miles down another road after a 90-degree turn

These two segments form a right triangle where both legs are 2 miles. We need to calculate the hypotenuse, which would represent the direct distance to the grocery store.

Using the Pythagorean theorem:

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

where \(a = 2\) miles and \(b = 2\) miles.

Substituting the values:

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

So, the direct distance to the store is approximately 2.8 miles.

Now we can calculate the distance he actually traveled:

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

To find the distance saved by taking the direct route, we subtract the direct distance from the traveled distance:

\[ 4 \text{ miles} - 2.8 \text{ miles} = 1.2 \text{ miles} \]

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