Answer:
3 units
Step-by-step explanation:
In a 30-60-90 triangle, the length are given by:

Where the longest side x, is the hypotenuse.
The shortest side is

Since x=6 is the hypotenuse, the shortest side length is:

Length is 3 times the width
So L = 3W
If L is decreased by 4m and with increased by 1m and perimeter is 66 then
2(3W - 4) + 2(W + 1) = 66
6W - 8 + 2W + 2 = 66
8W - 6 = 66
8W = 72
W = 9
L = 3 x 9 = 27
Width of rectangle = 9 m and length = 27 m
New rectangle:
Width is increase by 1 m = 9 + 1 = 10 m
Length is decreased by 4 m = 27 - 4 = 23 m
Answer
Dimensions of new rectangle are 10 m and 23 m
I’m not sure if you meant to put them in fraction form or not, but if you meant to put them as fractions (4 3/5) (6 1/5) then the answer would be
46.81