Answer:
x = 14
Step-by-step explanation:
Similar triangles have the property that the measure of its corresponding sides is proportional.
This can be written as:
[tex]\displaystyle \frac{x+1}{27}=\frac{5}{x-5}[/tex]
Cross-multiplying the fractions:
[tex](x+1)(x-5)=27(5)[/tex]
Operating:
[tex]x^2-4x-5=135[/tex]
[tex]x^2-4x-140=0[/tex]
Factoring:
(x-14)(x+10)=0
Solving:
x=14, x=-10
Only positive values can be accepted for x, thus:
x = 14
