The value of the sides are 12 and 13
Using the Pythagorean theorem, we have that the hypotenuse square is equal to the square of the other two sides.
Then, we have that the two consecutive integers are;
Hypotenuse = x + 1
Other sides are x and 5
(x + 1)² = 5² + x²
expand the bracket, we get;
x² + 2x + 1 = 25 + x²
collect the like terms, we get;
2x +1 = 25
2x = 24
Divide both sides by the coefficient of x, we get;
x = 24/2
Divide the values
x =12
Hence, the value of the sides are 12 and 13
Complete question