Look at the picture.
Use the Pythagorean theorem:
[tex]a^2+b^2=d^2[/tex]
A) a = 1, b = 1
[tex]d^2=1^2+1^2\\\\d^2=1+1\\\\d^2=2\to d=\sqrt2\ \text{it's not rational number}[/tex]
B) a = 4, b = 5
[tex]d^2=4^2+5^2\\\\d^2=16+25\\\\d^2=41\to d=\sqrt{41}\ \text{it's not rational number}[/tex]
C) a = 3, b = 4
[tex]d^2=3^2+4^2\\\\d^2=9+16\\\\d^2=25\to d=\sqrt{25}\to d=5\ \boxed{:)}[/tex]
D) a = 1, b = 2
[tex]d^2=1^2+2^2\\\\d^2=1+4\\\\d^2=5\to d=\sqrt5\ \text{it's not rational number}}[/tex]
Answer: C) a = 3, b = 4.
