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

Question 586647: A smaller commuter airline flies to three cities whose locations form a 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.....
Found 2 solutions by zoomkaboom4, Alan3354:
Answer by zoomkaboom4(62) (Show Source): You can put this solution on YOUR website!
Since it is a right triangle, the other two cities are 400 miles apart because..
400+400+600 = 1400 miles.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A smaller commuter airline flies to three cities whose locations form a 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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The hypotenuse = 600 miles
The other 2 legs, a & b, add to 800 miles
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a + b = 800
b = 800 - a
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=80000 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 541.42135623731, 258.57864376269. Here's your graph:

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