Answer:
x = 7.5
Step-by-step explanation:
Since the midsegment and the third segment of the triangle are parallel to each other, therefore,
[tex] \frac{8 + 10}{8} = \frac{6 + x}{6} [/tex]
[tex] \frac{18}{8} = \frac{6 + x}{6} [/tex]
[tex] \frac{9}{4} = \frac{6 + x}{6} [/tex]
Cross multiply
[tex] 9*6 = 4(6 + x) [/tex]
[tex] 54 = 24 + 4x [/tex]
Subtract 24 from each side
54 - 24 = 4x
30 = 4x
Divide both sides by 4
30/4 = x
7.5 = x
x = 7.5
