To find out how much distance Keith would have saved by riding directly to the grocery store instead of taking the two roads, we can use the Pythagorean theorem.
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Routes taken:
- He rode 2 miles down one road.
- Then he took a 90-degree turn and rode another 2 miles down a different road.
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Applying the Pythagorean theorem:
- If we consider the two roads he took as two sides of a right triangle (with each side being 2 miles), then we can find the direct distance to the grocery store, which would be the hypotenuse of the triangle.
- Let \( a = 2 \) miles and \( b = 2 \) miles.
- The hypotenuse \( c \) can be calculated as follows: \[ c = \sqrt{a^2 + b^2} = \sqrt{2^2 + 2^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} \approx 2.828 \text{ miles} \]
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Distance saved:
- The total distance Keith rode was \( 2 + 2 = 4 \) miles.
- The distance he would have saved by riding directly to the store is: \[ \text{Distance saved} = \text{Total distance} - \text{Direct distance} = 4 - 2.828 \approx 1.172 \text{ miles} \]
- Rounding that to the nearest tenth gives approximately 1.2 miles.
Therefore, the answer is 1.2 miles.
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