recall pythagorean theorem [tex]a {}^{2} + b {}^{2} = c {}^{2} [/tex] where and and b are the legs of the right triangle and c is the hypotenuse
[tex]4 {}^{2} + 4 {}^{2} = d {}^{2} [/tex] apply Pythagorean theorem [tex] \sqrt{16 + 16 } = d[/tex] square each 4 and take the square root of both sides [tex] \sqrt{32} = d[/tex] simplify
reduce the radical FINAL ANSWER [tex]4 \sqrt{2} = d[/tex]
or you can simply see that it's a 45 45 90 triangle and know that the hypotenuse d equal one of the legs times the square root of 2
