a) Angles ACB in ∆ABC and ECD in ∆EDC are congruent, since they form a vertical angle pair.
Angles ABC and EDC are clearly congruent, since they are both right angles.
The legs AB and ED are parallel, so angles BAC and DEC are congruent alternating interior angles.
Then ∆ABC is similar to ∆CDE by the angle-angle-angle postulate.
b) Because they're similar, corresponding sides occur in a fixed ratio, which tells us that
CD/BC = ED/AB
p/(5 cm) = (4 cm)/(6 cm)
p = 10/3 cm