Answer:
GH = 17
Step-by-step explanation:
Given that H is the midpoint of segment GI, and GH = 5x + 2, HI = 9x - 10, GH is congruent to HI. This implies GH = HI.
Therefore:
[tex] GH = HI [/tex], which will give us the following equation:
[tex] 5x + 2 = 9x - 10 [/tex]
Solve for x
[tex] 5x + 2 - 9x = 9x - 10 - 9x [/tex] (subtracting 9x from each side)
[tex] -4x + 2 = -10 [/tex]
[tex] -4x + 2 - 2 = -10 - 2 [/tex] (subtracting 2 from each side)
[tex] -4x = -12 [/tex]
[tex] \frac{-4x}{-4} = \frac{-12}{-4} [/tex] (dividing both sides by -4)
[tex] x = 3 [/tex]
GH = 5x + 2
Plug in the value of x
GH = 5(3) + 2 = 15 + 2
GH = 17
