Answer:
AE = 26 units
Step-by-step explanation:
Given that ABC is congruent to EDC, therefore, the corresponding angles and corresponding lengths of ∆ABC and ∆EDC are equal to each other in measure.
AE = 2(AC) = 2(CE) or
AE = AC + CE
Let's find the AC using Pythagorean Theorem, since the ∆s are both right triangles.
BA is congruent to DE.
Since DE = 12 units, therefore, BA = 12 units.
BC = 5 units (given)
Using Pythagorean Theorem:
AC² = BA² + BC²
AC² = 12² + 5² (substitution)
AC² = 144 + 25 = 169
AC = √169
AC = 13 units
Since ∆ABC = ∆EDC, therefore:
AE = 2(AC)
AE = 2(13)
AE = 26 units
