The hikers hiked 3 miles from the trailhead to the waterfall. they made a right turn and hiked 3 miles until they stopped for lunch. about how many miles do they need to hike back to get to the trailhead

The hikers 3 miles from the trailhead to the waterfall.
d1 = 3 miles

Then, the hikers made a right turn and hiked another 3 miles until they stopped for lunch.
d2=3 miles

We can solve the distance when they returned to the trailhead using Pythagorean theorem:
D ² =d1² + d2²
D² = 3² + 3²
D = 4.24

The distance is 4.24 miles. 

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