G lies on the perpendicular bisector of segment AB, AG = x2 + 4x, and BG = x + 18. Find AG
since G is on the perpendicular bisector of AH, then AG=BG. set the two equations as equal to each other and then solve
3 or -6
To find the length of segment AG, we can start by setting the lengths of AG and BG equal to each other since G lies on the perpendicular bisector of segment AB.
AG = BG
Now, let's substitute the given expressions for AG and BG into this equation:
x^2 + 4x = x + 18
Next, we need to solve this quadratic equation to find the value of x. We can start by rearranging the equation to bring all the terms to one side:
x^2 + 4x - x - 18 = 0
Combining like terms, we have:
x^2 + 3x - 18 = 0
Now, we can factor this quadratic equation or use the quadratic formula to solve for x. By factoring, we find:
(x + 6)(x - 3) = 0
Setting each factor equal to zero:
x + 6 = 0 or x - 3 = 0
Solving each equation, we find that x = -6 or x = 3.
Since the length cannot be negative, we can conclude that x = 3.
Now, let's substitute this value of x back into the expression for AG to find the length of segment AG:
AG = x^2 + 4x
= (3)^2 + 4(3)
= 9 + 12
= 21
Therefore, the length of segment AG is 21.