# 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

#### Explanation:

Pythagoras' theorem tells us that the sides of a right angled triangle with legs of length

#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+2 = n+(n+1)#

Subtracting

#1 = n#

So the only solution is