Answer:
The length of the missing segment is 44
Step-by-step explanation:
Given
The figure above
Required
Determine the missing segment
Let the missing segment be represented with x
Given that, there exist parallel lines between the two triangles;
The relationship between the sides of the triangles is as follows;
[tex]\frac{20}{x} = \frac{10+20}{22+x}[/tex]
[tex]\frac{20}{x} = \frac{30}{22+x}[/tex]
Cross Multiply
[tex]20 * (22 + x) = 30 * x[/tex]
Open bracket
[tex]20 * 22 + 20 * x = 30 * x[/tex]
[tex]440 + 20x = 30x[/tex]
Subtract 20x from both sides
[tex]440 + 20x - 20x= 30x- 20x[/tex]
[tex]440 = 30x- 20x[/tex]
[tex]440 = 10x[/tex]
Divide both sides by 10
[tex]\frac{440}{10} = \frac{10x}{10}[/tex]
[tex]\frac{440}{10} = x[/tex]
[tex]44 = x[/tex]
[tex]x = 44[/tex]
Hence, the length of the missing segment is 44
