Question

caden is deep - sea diving with bernie, who is to the south of him. a fish emerges from a hole to the east of bernie. the fish swims 7 meters to bernie and then swims 7 meters to caden. the fish then swims back to its hole and disappears. how far did the fish travel in all? if necessary, round to the nearest tenth. meters

Explanation:

Step1: Determine the shape of the path

The path of the fish forms a right - angled isosceles triangle. Let the distance from the hole to Bernie be \(a = 7\) meters, from Bernie to Caden be \(b = 7\) meters. By the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(c\) is the distance from Caden to the hole.

Step2: Calculate the distance from Caden to the hole

Substitute \(a = 7\) and \(b = 7\) into the Pythagorean theorem:

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Step3: Calculate the total distance

The fish swims \(7\) meters (hole - Bernie), \(7\) meters (Bernie - Caden), and approximately \(9.9\) meters (Caden - hole). The total distance \(d=7 + 7+9.9\)

Answer:

\(23.9\) meters