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 -112
32x = 38x-112
Subtracting 38x from both sides, we get
32x-38x = 38x-38x-112
-6x = -112
Dividing 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].
