To determine if it is possible for AB = 10, BC = 2x + 5, and AC = 5x, given that point B is the midpoint, we need to examine the given information and conditions.
The length of AB is given as 10.
BC is expressed as 2x + 5, where x represents an unknown value.
AC is expressed as 5x.
Since point B is the midpoint, this implies that the lengths of AB and BC are equal. Therefore, we can set up the equation:
2x + 5 = 5x
Now we can solve this equation to find the value of x:
2x + 5 = 5x
5 = 5x - 2x
5 = 3x
x = 5/3
So, we found the value of x to be 5/3.
However, we also have the given condition that AB is equal to 10. Substituting the value of x into the equation for AC, we can check if this condition is satisfied:
AC = 5x
AC = 5 * (5/3)
AC = 25/3
The length of AC is 25/3, which is not equal to 10.
Therefore, it is not possible for AB to be 10, BC to be 2x + 5, and AC to be 5x, given that point B is the midpoint.