value of x = 8
Explanation:
Two lines are parallel. The triangles are similar, so we can use similar triangles theorem:
The ratio of corresponding sides are equal.
[tex]\frac{x}{4+x}=\frac{10}{10\text{ + 5}}[/tex][tex]\begin{gathered} \frac{x}{4+x}=\frac{10}{15} \\ \text{cross multiply:} \\ 15(x)\text{ = 10(4 + x)} \end{gathered}[/tex][tex]\begin{gathered} 15x\text{ = 10(4) + 10(x)} \\ 15x\text{ = 40 + 10x} \\ \text{subtract 10x from both sides:} \\ 15x\text{ - }10x\text{ = 40 + 10x - 10x} \end{gathered}[/tex][tex]\begin{gathered} 5x\text{ = 40} \\ \text{divide both sides by 5:} \\ \frac{5x}{5}=\frac{40}{5} \\ x\text{ = 8} \end{gathered}[/tex]
