Respuesta :
Answer
8
Explanation
The right triangle side lengths must satisfy the right triangle inequality which says that if a triangle has side lengths A, B, and C then the sum of any two side lengths must be greater than the measure of the third side
[tex]A+B>C[/tex]In our case, the side lengths 8, x, and x + 2 must satisfy this condition and therefore, we arrange the inequality such that the solution for x is a positive number (side lengths cannot be negative)
The right arrangement that satisfies the triangle inequality is
[tex]x+x+2>8[/tex]Let us solve for x to see which side length is the hypotenuse (the largest side length is the hypotenuse)
The left-hand side of the above inequality simplifies and gives us
[tex]2x+2>8[/tex]subtracting 2 from both sides gives
[tex]2x>6[/tex]Finally, dividing both sides by 2 gives
[tex]x>3[/tex]This means one side length is greater than 3, the other side length x + 2 is, therefore, greater than 5, and the third side length is 8.
Hence, the longest side length is 8, and therefore, it is the right answer.
