Scenario 1: You and your friend enjoy riding your bicycles. Today is a beautiful sunny day, so the two of you are taking a long ride out in the country side. Leaving your home in Sunshine, you ride 6 km due west to the town of Happyville, where you turn south and ride 8 km to the town of Crimson. When the sun begins to go down, you decide that it is time to start for home. There is a road that goes directly from Crimson back to Sunshine. If you want to take the shortest route home, do you take this new road, or do you go back the way you came? Justify your decision. How much further would the longer route be than the shorter route? Assume all roads are straight.

Question

Scenario 2: A newly-planted tree needs to be staked with three wires. Each wire is attached to the trunk 3 m. above the ground, and then anchored to the ground 4 m. from the base of the tree. How much wire is needed for 6 trees?
Scenario 3: Jill’s front door is 98 cm wide and 190cm tall. She purchased a circular table that is 96 cm in diameter. Will the table fit through the front door? Determine the radius of the largest table that will fit through the door? Explain using mathematics.

Answer 1

#1. You have gone two sides of a right triangle.
The 3rd side (in this case, the hypotenuse) of any triangle is less than the sum of the other two sides.
Go direct.

Any ideas on the others?