Question

The number of right triangles with sides of lengths \[\sqrt{n+1}\], \[\sqrt{n+2}\], and \[\sqrt{n+3}\] is:
a) 0 b) 1 c) 2 d) 3 e) unbounded

Answer 1

\(\sqrt{n+3}\) is the longest side, so its the hypotenuse.
now apply pythagoras theorem.

Answer 2

\[\sqrt{n+1}^{2}+\sqrt{n+2}^{2}=\sqrt{n+3}^{2}\]

Answer 3

(n+1)+(n+2)=(n+3)

Answer 4

yeah, how many values of 'n' satisfy that equation ?

Answer 5

2n+3=n+3
n=0

Answer 6

number of right triangles = number of values of n

Answer 7

0 right triangles?

Answer 8

no, n=0 is one value of n.
so there's one right triangle with side, sqrt 1 sqrt 2 and sqrt 3

Answer 9

oh, so there is 1 right triangle, where n = 0

Answer 10

yup.

Answer 11

Thank you! :)