The length of the line connecting two places is the distance between them.
If the two points are on the same horizontal or vertical line, the distance can be calculated by subtracting the non-identical values.
To find what is the distance from E to side AD:
If you draw a diagram, you'll see that triangle AEB is a right triangle with lengths 5, 12, and 13.
Let's call F the point where E meets side AD, so the problem is to find the length of EF.
By Angle-Angle Similarity, triangle AFE is similar to triangle BEA. (the right angles are congruent, and both angle FAE and ABE are complementary to angle BAE)
Since they're similar, the ratios of their side lengths are the same.
EF/EA = EA/AB (they're corresponding side lengths of similar triangles).
Substitute them with known lengths:
EF/5 = 5/13
EF = 5 × (5/13) = 25/13
Therefore, the distance from E to side AD is 25/13.
The correct answer is given below: Square ABCD has side lengths of 13 units. Point E lies in the interior of the square such that AE=5 units and BE=12 units. What is the distance from E to side AD? Express your answer as a mixed number.
