Triangle Problem
(Raleigh Durham Chapel hill)
In the state of North Carolina, a specific region in the piedmont areas is known as the research triangle
or just Triangle because its general geographic region is contained in three cities: Raleigh (Approximate
population: 380, 173), Durham (approximate population: 479, 624), and chapel Hill (approximate
population: 54, 492). Imagine you are on the board that will decide on where the stadium will be
located and the planner has presented two options.
Option 1: Place the stadium the same distance from each of the three cities. If this
option isselected the state will need to pay to build three new highways from
each city to the stadium.
Option 2: Place the stadium equidistant from the three existing highways. The
existinghighways would need to be resurfaced and new highways built from each
existing highway tothe stadium.
Assume the cost of building new highways is $125,000 per mile and the cost of
resurfacing an existing highway is $50,000 per mile.
Assume that 1cm is to 2 miles
Questions: Answer the questions below in as detailed a manner as possible
1. For each option, describe how you used your DGE to determine a location
for the stadium.Include a screenshot that shows the three cities and a
proposed location for the stadium. Also, for each option, compute the cost
for road construction/resurfacing.
We found the circumcenter which by def. gives us the point that is equidistant from
each vertices of the triangle that is formed using the cities.
The location of the new stadium would be in Park Village
The cost of the new highways would be for
Option 1)
2∙m DA ∙3 ∙125000 = 9.57∙106 cm
Option 2)
50000 + 50000∙ 2∙ m OP + m PQ + m QG + m GH + m HI + m IJ
+
m AO + m JD ∙2 ∙125000 = 7.73∙106 cm
2. Which option would you choose? Explain.We would choose option 2
because it is dramatically cheaper than option 1. 7.73x10^6 is less than
9.57x10^6 for a difference of 1.84x10^6.
Extension
3. The planner has also suggested a third option that could take into
consideration the populations of the three cities. Describe a possible option
that uses population information to find a site for the stadium.
I would build the stadium closest to the city with the largest population because
it would reduce the amount of new construction of highways.
4. Create a different, fourth option. Describe and explain how it compares to
the other three options.
I would use the centroid because the stadium would be placed closest to
Durham and Chapel which already have preexisting highways and also have
a much larger and contained population then Raleigh. Also Raleigh has a
highway that already can serve as a means to commute to the location of the
stadium.
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