In order to find the perimeter of triangle ELD, we first need to determine the lengths of the sides EL, LD, and DE.

1. Finding the length of EL:
Since DN is the perpendicular bisector of AC, it divides AC into two congruent segments. Therefore, AD = DC. Similarly, since EM is the perpendicular bisector of AB, it divides AB into two congruent segments. Therefore, AE = EB.
Since ABC is a triangle with BC = 24 and angle A = 60 degrees, we can use the Law of Sines to find the length of AB.
sin A / AB = sin B / BC
sin 60° / AB = sin B / 24
√3 / AB = sin B / 24
AB = (24 * √3) / sin B
Since AE = EB, we have EL = (AB - AE) / 2 = (AB - AB) / 2 = 0.

2. Finding the length of LD:
Since DN is the perpendicular bisector of AC, DN is also the altitude of triangle ADC. Therefore, triangle ADC is a right-angled triangle with angle A = 60 degrees and angle D = 90 degrees. Thus, triangle ADC is a 30-60-90 triangle, and we can use the ratios of the sides to find the length of AD and DC.
Let AD = x, then DC = x.
In a 30-60-90 triangle, the ratio of the sides is x : x√3 : 2x.
Therefore, AD = DC = x = 24 / 2 = 12.
Since L is the midpoint of MN, we have LD = MN / 2.

3. Finding the length of DE:
Since EM is the perpendicular bisector of AB, EM is also the altitude of triangle ADE. Therefore, triangle ADE is a right-angled triangle with angle A = 60 degrees and angle E = 90 degrees. Thus, triangle ADE is a 30-60-90 triangle, and we can use the ratios of the sides to find the length of AE and DE.
Let AE = y, then DE = y√3.
In a 30-60-90 triangle, the ratio of the sides is y : y√3 : 2y.
Therefore, AE = y = 24 / 2√3 = 4√3.
Since L is the midpoint of MN, we have LE = MN / 2.

4. Finding the perimeter of triangle ELD:
The perimeter of triangle ELD is EL + LD + DE.
Since EL = 0, we only need to find the lengths of LD and DE.
LD = MN / 2 = 12 / 2 = 6.
DE = y√3 = 4√3√3 = 4 * 3 = 12.
Therefore, the perimeter of triangle ELD is 0 + 6 + 12 = 18 units.