Answer:
11.4
Step-by-step explanation:
So we know that Triangle ACB is similar to Triangle EFD.
This means that their sides are proportional to each other.
We want to find x or side AB. To do so, we can set up a proportion.
The proportional side to AB is ED. Let's also use BC since we know its value. The proportional side to BC is DF. Thus:
![\frac{AB}{ED}=\frac{BC}{DF}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7BED%7D%3D%5Cfrac%7BBC%7D%7BDF%7D)
Substitute x for AB, 3.8 for Ed, 15 for BC, and 5 for DF. Thus:
![\frac{x}{3.8}=\frac{15}{5}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B3.8%7D%3D%5Cfrac%7B15%7D%7B5%7D)
Reduce the right:
![\frac{x}{3.8}=\frac{3}{1}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B3.8%7D%3D%5Cfrac%7B3%7D%7B1%7D)
Cross multiply:
![x=11.4](https://tex.z-dn.net/?f=x%3D11.4)
So, the value of x is 11.4
And we're done!