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.
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