let

a = the width of the trailer, a>0

b = the length of the trailer, b>0

a = the height of the trailer

the surface area is 928 ft^2:

2(a*b + a*b + a*a) = 928

2a*b + a^2 = 928/2

2ab + a^2 = 464

the sum of all edges of the trailer is 164 ft:

8a + 4b = 164 divide both sides by 4

2a + b = 41

b = 41 - 2a

plug b = 41 - 2a into 2ab + a^2 = 464 we have:

2a(41 - 2a) + a^2 = 464

by solving we find:

a1 = 8 ft

a2 = 19.33 ft

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for a = 8 ft we have b = 41 - 2*8 = 35 ft.

for a = 19.33 ft we have b = 41 - 2*19.33 = 2.34 ft.

the dimensions of the trailer are: the length is 35 ft, the width and the height are 8 ft each.