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 miles due west to the town of Happyville, where you turn south and ride 8 miles 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.

Scenario 2) A newly-planted tree needs to be staked with three wires. Each wire is attached to the trunk 3 ft. above the ground, and then anchored to the ground 4 ft. from the base of the tree. How much wire is needed for 6 trees?

Scenario 3) Jill’s front door is 42” wide and 84” tall. She purchased a circular table that is 96 inches in diameter. Will the table fit through the front door? Explain using approximations.

4 answers

(1)hypotenuse = straight home
sqrt(36+64) = 10
straight is 10 miles
same way is 6+8 = 14 miles

(2) hypotenuse of 3,4 5 right triangle is 5
5*6 = 30
plus enough for the knots :)

(3)diagonal (hypotenuse) length is the longest

sqrt (42^2 + 84^2) = 93.9, so no

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