Answer:
[tex]x=7.9[/tex]
Step-by-step explanation:
We have been given an image of two triangles. We are also told that AE||BD. We are asked to find the value of x.
Upon looking at our given diagram, we can see that both triangle shares a common angle that is angle C.
Since line AE is parallel to line BD, so angle A will be equal to angle B and angle E will be equal to angle D by corresponding angles of parallel lines.
Since both triangles have same angle measure, therefore, both triangles are similar.
We know that corresponding sides of similar triangles are proportional, so we can set an equation as:
[tex]\frac{x}{11}=\frac{5}{7}[/tex]
[tex]\frac{x}{11}*11=\frac{5}{7}*11[/tex]
[tex]x=\frac{5*11}{7}[/tex]
[tex]x=\frac{55}{7}[/tex]
[tex]x=7.857142857\approx 7.9[/tex]
Therefore, the value of x is is approximately 7.9 units.
