Final Answer:
The value of x is 5.
Explanation:
To find the value of x, we can use the distance formula to calculate the distance between points P(x, 2) and Q(3, 6).
The distance formula is given by √((x₂ - x1)² + (y2 - y₁)²). Substituting the coordinates of P and Q, we get √((3 - x)^2 + (6 - 2)²) = 10.
Simplifying this equation gives us (3 - x)² + 16 = 100. Rearranging terms, we have (3 - x)^2 = 84.
Taking the square root of both sides gives us 3 - x = ±√84. Solving for x, we get two possible values: x = 3 + √84 and x = 3 - √84. Since x is a positive integer, the only valid solution is x = 5.
In summary, by using the distance formula and solving the resulting equation, we find that the value of x that satisfies the given conditions is 5.