Side lengths of an right triangle are sqrtn, sqrt(n+1), and sqrt(n+2). How do you find n?

1 Answer
Mar 16, 2018

n=1

Explanation:

Pythagoras' theorem tells us that the sides of a right angled triangle with legs of length a, b and hypotenuse of length c satisfy:

c^2 = a^2 + b^2

So in our example, we require:

(sqrt(n+2))^2 = (sqrt(n))^2+(sqrt(n+1))^2

Assuming n >= 0, this simplifies to:

n+2 = n+(n+1)

Subtracting n+1 from both sides, this becomes:

1 = n

So the only solution is n = 1, giving us a triangle with sides 1, sqrt(2) and sqrt(3).