Posted by Barb on Saturday, February 2, 2013 at 3:12am.
Prove that no isosceles right triangle exists whose sides are integers.

MathPlease help  Reiny, Saturday, February 2, 2013 at 8:59am
let the shorter sides be x units each ,
let the hypotenuse be h
(clearly we can't have the equal sides being the hyppotenuses, or else we would have 2 right angles, leaving nothing left for the third angle)
h^2 = x^2 + x^2
h^2 = 2x^2
h = √2x
so whatever integer x is, multiplying an integer by √ makes it irrational, thus no longer an integer.
Answer This Question
Related Questions
 geometry  The sides of a triangle are 8,15 and 18 the shortest side of a ...
 GEOMETRY  The sides of a triangle are 8,15 and 18 the shortest side of a ...
 geometry easy  The sides of a triangle are 8,15 and 18 the shortest side of a ...
 geometry triangles  The sides of a triangle are 8,15 and 18 the shortest side ...
 Math (Geometry)  The perimeter of right triangle ABC is equal to the perimeter ...
 Math  If all of the following triangles have the same perimeter, which has the ...
 Math  Can someone please check to see if I answered these true and false ...
 geometry  The perimeter of right triangle RST is equal to the perimeter of ...
 Math  Decide whether each statement is always true, sometimes true, or never ...
 GEOMETRY  Which statement is the contrapositive of the following conditional: ...
More Related Questions