From the triangle given, we are required to solve for x and y.
Since they are similar triangles, let's find x and y below.
For x:
[tex]\frac{5}{8}=\frac{5+x}{10}[/tex]
Let's find x, from the equation above.
Cross multiply:
[tex]\begin{gathered} 8(5+x)=10(5) \\ \\ 40+8x=50 \\ \\ \text{Subtract 40 from both sides:} \\ 40-40+8x=50-40 \\ \\ 8x=10 \end{gathered}[/tex]
Divide both sides by 8:
[tex]\begin{gathered} \frac{8x}{8}=\frac{10}{8} \\ \\ x=1.25 \end{gathered}[/tex]
For y:
[tex]\begin{gathered} \frac{7}{8}=\frac{7+y}{10} \\ \\ 8(7+y)=7(10) \\ \\ 56+8y=70 \\ \\ 8y=70-56 \\ \\ 8y=14 \\ \\ \frac{8y}{8}=\frac{14}{8} \\ \\ y=1.75 \end{gathered}[/tex]
ANSWER:
x = 1.25, y = 1.75
