This question is suppose to be simple but i keep getting it wrong

Question

Triangle LMN has vertices L(1, 6), M(6, 3) and N(5, 7). What type of triangle is Triangle LMN? Select all that apply

Scalene triangle
Right triangle
Isosceles triangle
Equilateral triangle
Obtuse triangle
Acute triangle

I got Isosceles Triange and acute but i keep getting it worong

Answer 1

LM = √(5^2+3^2) = √34
LN = √(4^2+1^2) = √17
MN = √(1^1+4^2) = √17

So, it is isosceles.
But since

√17^2 + √17^2 = √34^2
17+17 = 34

it is a right triangle.

Answer 2

How do you know its a right angle when the answer is 34 i thought it has to be 90?

Answer 3

I'm not talking about angles, but sides. Remember the Pythagorean Theorem?

a^2 + b^2 = c^2