Question
If sides of right angled triangle are three consecutive integers.then length of smallest side is
Answers
Reiny
the simplest right-angled triangle has sides
3,4, and 5
If you did not know that,
let the three sides be
x, x+1, and x+2
x^2 + (x+1)^2 = (x+2)^2
x^2 + x^2 + 2x + 1 = x^2 + 4x + 4
x^2 - 2x - 3 = 0
(x-3)(x+1) = 0
x = 3 or x = -1, the last one is silly
x=3
conclusion ....
3,4, and 5
If you did not know that,
let the three sides be
x, x+1, and x+2
x^2 + (x+1)^2 = (x+2)^2
x^2 + x^2 + 2x + 1 = x^2 + 4x + 4
x^2 - 2x - 3 = 0
(x-3)(x+1) = 0
x = 3 or x = -1, the last one is silly
x=3
conclusion ....