in the figure below, the segment is parallel to one side of the triangle. Find the value of x.

Answer: x= .[tex]18\frac{2}{3}[/tex].
Step-by-step explanation: We are given a segment parallel to the base.Therefore, sides of big triangle and small triangles would be in proportion.[tex]\frac{One \ Side \ of\ big \ triangle }{One \ Side \ of\ small \ triangle} =\frac{Other \ Side \ of\ big \ triangle }{Other \ Side \ of\ small \ triangle}[/tex]Setting values for the shown triangle, we get [tex]\frac{x+(x+7)}{x} =\frac{16+22}{22}[/tex][tex]\frac{2x+7}{x} =\frac{38}{16}[/tex]On cross multiplication, we get 16(2x+7) = 38(x)32x + 112 = 38x.Subtracting 112 from both sides, we get 32x + 112-112 = 38x -11232x = 38x-112Subtracting 38x from both sides, we get 32x-38x = 38x-38x-112-6x = -112Dividing both sides by -6, we get [tex]\frac{-6x}{-6} =\frac{-112}{-6}[/tex]x= .[tex]18\frac{2}{3}[/tex].Therefore, x= .[tex]18\frac{2}{3}[/tex].