To find the distance across the lake, first consider that triangles ADE and ABC are congruent. Then, you have the relation between the following proportions of the two triangles:
[tex]\frac{x}{ED}=\frac{AC}{AE}[/tex]where:
AC = AE + EC = 25 ft + 30 ft = 55 ft
ED = 15 ft
AE = 25 ft
solve the equation for x and replace the values of the segments:
[tex]\begin{gathered} x=(ED)(\frac{AC}{AE}) \\ x=(15ft)(\frac{55ft}{25ft})=33ft \end{gathered}[/tex]x represents the distance across the lake.
Hence, the distance is 33 ft
