SOLUTION: Please help me solve this equation: In the annual Pythagoras Triathlon, competitors swim, bike, and run. Each portion of the race is the side of a right triangle. The run portion i

Question 805425: Please help me solve this equation: In the annual Pythagoras Triathlon, competitors swim, bike, and run. Each portion of the race is the side of a right triangle. The run portion is 1.12 miles, and the bike portion is 1.13 miles. When Russ heard someone say the swim portion represented the hypotenuse of the race course, he almost fainted. But then he learned that the hypotenuse was the bike portion, and he breathed a sigh of relief.
How much shorter is the swim portion than he originally thought?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Russ thought that the right triangle was like this (with the distances in miles):
That would make the swim portion longest, because the Pythagorean theorem says that

(rounded)
It turns out that the race is like this (drawing not to scale for good reason):
In this case, the Pythagorean theorem says that

(exactly)
The difference (rounded) is :

NOTE:
If I had made the last triangle to scale it would have been such a narrow, tall triangle that it would have been useless to illustrate the problem (so I made it wider).
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