Similar Triangles
Triangles ABC and ADE are similar which means their corresponding side lengths are in the same proportion.
The height of triangle ABC is 1
The height of triangle ADE is 5
The base of triangle ABC is x
The base of triangle ADE is x + 9
Therefore:
[tex]\frac{5}{1}=\frac{x+9}{x}[/tex]
Cross-multiplying:
[tex]\begin{gathered} 5x=x+9 \\ \\ Subtracting\text{ x:} \\ \\ 4x=9 \\ \\ Dividing\text{ by 4:} \\ \\ x=\frac{9}{4} \end{gathered}[/tex]
