Question

the club members hiked 3 kilometers north and 4 kilometers east, then went directly home as shown by the dotted line. how far did they travel to get home?

Explanation:

Step1: Identify the right - angled triangle

The path of the club members' hike forms a right - angled triangle, where the two legs of the right - angled triangle are 3 km (north) and 4 km (east).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem for a right - angled triangle is $a^{2}+b^{2}=c^{2}$, where $a = 3$ km and $b = 4$ km, and $c$ is the distance from the end - point of the hike to the starting point (home). So, $c=\sqrt{3^{2}+4^{2}}$.

Step3: Calculate the value of $c$

First, calculate $3^{2}=9$ and $4^{2}=16$. Then $3^{2}+4^{2}=9 + 16=25$. So, $c=\sqrt{25}=5$ km.

Answer:

5 km