Question

I'm stuck......

Directions: Choose one of the following scenarios. Use the space provided on the back of this sheet to sketch your scenario, solve using Pythagorean Theorem, and write a full explanation for your answer. Finally, use a separate sheet of paper to draw and color a model for your solution. Use the rubric as a guide.

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.

Answer 1

Lets visualise this

Answer 2

For scenario 1

You want to find the red part

Answer 3

I forgot to add the values for each, we know the "sides" so we have to solve for the hypotenuse. Do you know the Pythagorean Theorem?

Answer 4

I'm not sure.....8^2+6^2?

Answer 5

Yes you have the right idea, Pythagorean theorem is
\(a^2+b^2=c^2\) c being the hypotenuse

Answer 6

So we would have \(6^2+8^2=c^2\)
Lets solve for C

Answer 7

100?

Answer 8

Almost, we have
\(100=c^2\)
We still have to do the square root of both sides

Answer 9

?

Answer 10

We have to get c by itself (it is to the second power right now)

\(\sqrt{100}=\sqrt{c^2}\)

Answer 11

10

Answer 12

Right so the travel would be 10 miles, that is the measure of the shortest distance, to find the longer distance we add 6 and 8 since that is the length of the original path

Answer 13

14

Answer 14

Now we can answer the question
"If you want to take the shortest route home, do you take this new road, or do you go back the way you came?"

Shortest route = 10 miles
Back the way we came = 14 miles

Answer 15

new road

Answer 16

Yes the new route, how would you justify it?

Answer 17

Because its the shortest route....

Answer 18

Yes basically, lol
"How much further would the longer route be than the shorter route?"
Do you know how would would solve for this?

Answer 19

4?

Answer 20

Right you would subtract, so the original route would be 4 miles longer

Answer 21

Thank you!