SOLUTION: A small commuter airline flies to 3 cities whose locations form the vertices of a right triangle. The total flight distance (from city A to city B to city C and back to City A) is

Algebra ->  Pythagorean-theorem -> SOLUTION: A small commuter airline flies to 3 cities whose locations form the vertices of a right triangle. The total flight distance (from city A to city B to city C and back to City A) is       Log On


   

Question 394108: A small commuter airline flies to 3 cities whose locations form the vertices of a right triangle. The total flight distance (from city A to city B to city C and back to City A) is 1400 miles. It is 600 miles between the two cities that are furthest apart. Find the other two distances between cities.
Answer by mananth(16949) About Me  (Show Source):
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A small commuter airline flies to 3 cities whose locations form the vertices of a right triangle. The total flight distance (from city A to city B to city C and back to City A) is 1400 miles. It is 600 miles between the two cities that are furthest apart. Find the other two distances between cities.
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ABC is a right triangle
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AB+BC+CA=1400 = perimeter of triangle
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The longest side in a right triangle is the hypotenuse.
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hypotenuse = 600
if one leg is x then the other leg = 1400-600-x= 800-x
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Use Pythagoras theorem
leg1^2 +leg2^2=Hyp^2
x^2+(1400-(600-x))^2=600^2
x^2+(800-x)^2=600^2
x^2+640000-1600+x^2=360000
2x^2-1600x+640000-360000=0
2x^2-1600x+280000=0
/2
x^2-800x+140,000=0
slove using quadratic equation
Find the roots of the equation by quadratic formula
a= 1 , b = -800 , c = 140,000
b^2-4ac= 80,000
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x1=%28800%2Bsqrt%2880000%29%29%2F%282%29
x= 541.42 miles
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x2=%28800-sqrt%2880000%29%29%2F%282%29
x2= 258.57 miles
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m.ananth@hotmail.ca