Shark Attack Write-up

by

Martha Burns

Guppy, Tadpole, and Goldfish beach surround Equilateral Sea. Why do you think Equilateral Sea is named that way?

Tiger shark and his family swim together in the Equilateral Sea. When the family gets hungry, Tiger makes sure they stay in one place (so he doesn't lose them), and then finds food at each of the beaches. Tiger gets food at one beach at a time because he can only hold so much food in his mouth at one time. So he gets food at one beach, comes back to share the food (red square), and then repeats the process at the other beaches.

Where should Tiger place his family in the Equilateral Sea in order to swim the least distance for his three hunting trips? Explain your reasoning.

Extension:

How would your answer change if Tiger placed his family on any given point inside the triangle?

How would your answer change if Tiger's family lived in the Scalene Sea?

Go to GSP and construct an equilateral triangle.  This is accomplished by constructing a line segment. Highlight one endpoint and the segment and construct a circle.  Highlight the other endpoint and the segment and construct a second circle.  The intersection of the two circles creates the third point necessary for an equilateral triangle. Connect the three points to construct the equilateral triangle.  How do you know this is an equilateral triangle?

Hide the circles by going to the Display button and clicking on Hide Circles.

Place a point randomly on each line segment and one point inside the triangle.  Connect the points and form three line segments.

Highlight each segment and take a measure of its length.

Take a sum of the three measures.

To find the least distance that Tiger shark needs to swim on his three hunting trips, move the inside point around and watch the sum of the three measures increase or decrease from the given measure.  The lowest value found is the place Tiger shark needs to place his family in the Equilateral Sea.