First let us assign the variables for the two lengths:
x = 1st integer
x + 1 = 2nd consecutive integer = the hypotenuse of the right triangle
The 2nd consecutive integer should be the hypotenuse since its value should be highest among the three sides.
Now using the hypotenuse formula we calculate for x:
(x + 1)^2 = 5^2 + x^2
x^2 + 2x + 1 = 25 + x^2
2x + 1 = 25
2x = 24
x = 12 m
So other integer is
x + 1 = 13 m
Therefore the other sides are 12 m and 13 m.
