In the triangle USI
US = 26+13
US=39
SI=39
IU=x
In triangle WSH
WS=26
SH=26
WH=20
Thus, we get :
[tex]\frac{WS}{SU}=\frac{HS}{SI}=\frac{26}{39}[/tex]Ratio of the two sides of triangle are same and the angle S is common
So, by SAS Similarity
Triangle USI and triangle WSh are similar
From the properties of similar triangle, the ratio of corresponding sides of triangle are always similar
So,
[tex]\begin{gathered} \frac{SW}{SU}=\frac{SH}{SI}=\frac{HW}{IU} \\ \text{Substitute the values} \\ \frac{26}{39}=\frac{26}{39}=\frac{20}{x} \\ \text{Simplify the last two} \\ \frac{26}{39}=\frac{20}{x} \\ x=\frac{20\times39}{26} \\ x=30 \end{gathered}[/tex]Answer: x = 30
