Answer:
The missing side “x” is 2.
Step-by-step explanation:
From the given figure, we came to know that these are “similar triangles” where the ratio of the one “corresponding side” of a triangle is equal to the other two “corresponding sides” of a triangle.
Let the triangles be ∆ABC and ∆DEF
![\Delta A B C \sim \Delta D E F](https://tex.z-dn.net/?f=%5CDelta%20A%20B%20C%20%5Csim%20%5CDelta%20D%20E%20F)
From similarity of triangle rule the sides,
![\frac{A B}{D E}=\frac{B C}{E F}](https://tex.z-dn.net/?f=%5Cfrac%7BA%20B%7D%7BD%20E%7D%3D%5Cfrac%7BB%20C%7D%7BE%20F%7D)
Given that,
AB = x, DE = 8, BC = 4 and EF = 16
![\text { Substitute the values in } \frac{A B}{D E}=\frac{B C}{E F} \text { to find }^{u} \mathrm{x}^{\prime \prime}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Substitute%20the%20values%20in%20%7D%20%5Cfrac%7BA%20B%7D%7BD%20E%7D%3D%5Cfrac%7BB%20C%7D%7BE%20F%7D%20%5Ctext%20%7B%20to%20find%20%7D%5E%7Bu%7D%20%5Cmathrm%7Bx%7D%5E%7B%5Cprime%20%5Cprime%7D)
![\frac{x}{8}=\frac{4}{16}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B8%7D%3D%5Cfrac%7B4%7D%7B16%7D)
![\frac{x}{8}=\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B8%7D%3D%5Cfrac%7B1%7D%7B4%7D)
![x=\frac{8}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B8%7D%7B4%7D)
x = 2
Therefore, we found the missing side x = 2