Question

Can someone help me find the valunof x?i bealive that is 8 but i need a little help?

Answer 1

value of x = 8

Step-by-step explanation:

Two lines are parallel. The triangles are similar, so we can use similar triangles theorem:

The ratio of corresponding sides are equal.

`(x)/(4+x)=\frac{10}{10\text{ + 5}}`
`\begin{gathered} (x)/(4+x)=(10)/(15) \\ \text{cross multiply:} \\ 15(x)\text{ = 10(4 + x)} \end{gathered}`
`\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}`
`\begin{gathered} 5x\text{ = 40} \\ \text{divide both sides by 5:} \\ (5x)/(5)=(40)/(5) \\ x\text{ = 8} \end{gathered}`