Answer:
[tex]x = 6[/tex]
Step-by-step explanation:
These right triangles are similar due to the Angle Angle Similarity Theorem.
This means their side lengths are proportional
We need to find the corresponding sides of the inner triangle and full right triangle.
7 corresponds with 7 and 3.5
4 corresponds with x.
Set up proportion.
[tex] \frac{4}{7} = \frac{x}{7 + 3.5} [/tex]
[tex] \frac{4}{7} = \frac{x}{10.5} [/tex]
[tex]42 = 7x[/tex]
[tex]x = 6[/tex]
