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.
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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=(-b+-sqrt(b^2-4ac))/(2a)}}}


{{{x1=(800+sqrt(80000))/(2)}}}
x= 541.42 miles
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{{{x2=(800-sqrt(80000))/(2)}}}
x2= 258.57 miles
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m.ananth@hotmail.ca