Three paths, $[AE]$, $[BE]$ and $[CD]$, have been constructed to provide access to a lake from a road $AC$ as shown in the diagram - Junior Cycle Mathematics - Question 9 - 2014

To find $|ED|$, we can use the property of similar triangles. Triangles $\Delta AEB$ and $\Delta ADC$ are similar because they share the angle at $A$ and both have a right angle. Therefore, their corresponding sides are proportional.

This can be expressed as:

$\frac{|AD|}{|AE|} = \frac{|CD|}{|BE|}$

Knowing the lengths of $|AE|$, $|BE|$, and $|CD|$, we can substitute these values into the proportion to solve for $|AD|$ first, and then find $|ED|$.