x = 6
Step-by-step explanation:
It's based on similarity of triangles
DEF ~ △XYZ
[tex] \implies \mathsf{ \frac{DE }{ XY } = \frac{EF}{YZ} = \frac{ FD}{ZX}}[/tex]
The sides should be taken in order, like the triangles start with DE and XY so, we'll proportionate DE and XY and then the next two sides and so on.
I'm using [tex] \mathsf{ \frac{DE }{XY } = \frac{EF}{YZ} }[/tex]to get the value of x.
[You can use any two fractions out of the three given above. ]
[tex] \implies \mathsf{ \frac{10}{x - 1} = \frac{8}{4} }[/tex]
[tex] \implies \mathsf{ \frac{10}{x - 1} = 2 }[/tex]
[tex] \implies \mathsf{ 10 = 2 (x - 1) }[/tex]
[tex] \implies \mathsf{ 10 = 2 x - 2 }[/tex]
[tex] \implies \mathsf{ 10 + 2= 2 x }[/tex]
[tex] \implies \mathsf{ 1 2= 2 x }[/tex]
[tex] \implies \mathsf{ x = 6 }[/tex]
Hence, the value of x is 6.
