indirect measurement : explain why the triangles are similar then find the distance represented by x.

Given data:
The given triangles.
The expression for the ratio of the corresponding sides is,
[tex]\begin{gathered} \frac{90\text{ yards}}{110\text{ yards}}=\frac{(90+90)\text{ yards}}{x} \\ \frac{9}{11}=\frac{180\text{ yards}}{x} \\ 9x=11\times(180\text{ yards)} \\ x=220\text{ yards} \end{gathered}[/tex]Thus, the value of x is 220 yards.