Answer:
x =2
Step-by-step explanation:
Similar triangles:-
- The given triangles are same shape but not necessarily the same size
- Corresponding angles are equal
- Corresponding sides are in the same ratio [tex]\frac{a}{p} = \frac{b}{q} = \frac{c}{r}[/tex]
Given diagram ΔABC AND ΔDBE are similar triangles.
[tex]\frac{BC}{BE} = \frac{AB}{BD}[/tex]
[tex]\frac{x+x+1}{x+1} = \frac{6+4}{6}[/tex]
on simplification , we get
[tex]\frac{2x+1}{x+1} = \frac{6+4}{6}[/tex]
cross multiplication , we get
12x+6 =10x +10
12x-10x = 10 -6
2x =4
x =2
Therefore the value of x =2
verification:-
[tex]\frac{BC}{BE} = \frac{AB}{BD}[/tex]
[tex]\frac{2x+1}{x+1} = \frac{6+4}{6}[/tex]
put x=2
[tex]\frac{2(2)+1}{2+1} = \frac{6+4}{6}[/tex]
[tex]\frac{5}{3} = \frac{6+4}{6}[/tex]
[tex]\frac{5}{3} = \frac{5}{3}[/tex]
both sides are equal
Therefore x value is 2
