(a) The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
We know that the width is 86m and the perimeter is 366m. Substituting these values into the formula, we get:
366 = 2l + 2(86)
Simplifying the right side, we get:
366 = 2l + 172
Subtracting 172 from both sides, we get:
194 = 2l
Dividing both sides by 2, we get:
l = 97
Therefore, the length of the rectangular field is 97m.
(b) The formula for the area of a rectangle is A = lw, where A is the area, l is the length, and w is the width.
We know that the length is 96cm and the area is 7200cm^2. Substituting these values into the formula, we get:
7200 = 96w
Dividing both sides by 96, we get:
75 = w
Therefore, the width of the rectangular painting is 75cm.