<u>Given</u>:
The given triangle QPO is a right triangle.
The length of QP is 5 units.
The length of OP is (x + 5) units.
The length of QO is (x + 6) units.
We need to determine the hypotenuse of the triangle QPO.
<u>Value of x:</u>
The value of x can be determined using the Pythagorean theorem.
Thus, we have;
Substituting the values, we get;
Expanding, we get;
Adding the like terms, we get;
Thus, the value of x is 7.
<u>Length of the hypotenuse:</u>
The hypotenuse of the triangle QPO is QO.
Substituting x = 7 in the length of QO, we get;
Thus, the length of the hypotenuse is 13 units.
Hence, Option D is the correct answer.