Answer:
[tex] x= 5*400 ft = 2000 ft[/tex]
Step-by-step explanation:
For this case we can use the figure attached and we are interested in order to find the value of x.
We have two similar triangles (DEC and ABC) and we can find the scale factor like this:
[tex]Factor= \frac{EC}{BC}=\frac{500ft}{100ft}=5[/tex]
And now we can apply proportions in order to find the value of x using the two sides DE and BA, since we have the ratio between the triangle DEC and ABC we have this:
[tex]Factor=5=\frac{x ft}{400 ft}[/tex]
And solving for x we got:
[tex] x= 5*400 ft = 2000 ft[/tex]
And then the distance across the lake would be 2000 ft
