anonymous
  • anonymous
Find all right triangles having sides with integral lengths that form an arithmetic sequence. ... and that is all it says ... :??
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
what grade / course is this for?
anonymous
  • anonymous
Pre-calculus, sorry, this answer is a little late. We just finished a unit on vectors, if that's helpful...
jim_thompson5910
  • jim_thompson5910
Let A, B, C be the sides of the triangle Furthermore, let A = x B = x+d C = x+2d By the pythagorean theorem A^2 + B^2 = C^2 Plug in the given values and solve for x x^2 + (x+d)^2 = (x+2d)^2 x^2 + x^2 + 2xd + d^2 = x^2 + 4xd + 4d^2 2x^2 + 2xd + d^2 = x^2 + 4xd + 4d^2 2x^2 + 2xd + d^2 - x^2 - 4xd - 4d^2 = 0 x^2 - 2xd - 3d^2 = 0 (x + d)(x - 3d) = 0 x+d = 0 or x-3d = 0 x = -d or x = 3d Now if the side lengths are integers, then d must be an integer Assuming that x is the smallest side length and all side lengths are positive (negative side lengths do not make sense), this means that x = -d is not possible. So the only solution is x = 3d So this means that the smallest side length is x = 3(1) = 3 So the smallest triangle possible is a 3,4,5 triangle Any other triangle that fits this description will be multiples of 3,4,5

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anonymous
  • anonymous
Thank you!
jim_thompson5910
  • jim_thompson5910
you're welcome

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