Let's factor the quadratic expression x² + 8x + 15 to find the length and breadth of the rectangular field:
x² + 8x + 15 = (x + 3)(x + 5)
Therefore, the length of the rectangular field is (x + 5) m and the breadth is (x + 3) m.
To find the perimeter of the rectangular field, we add up the lengths of all four sides:
Perimeter = 2(length + breadth)
Perimeter = 2[(x + 5) + (x + 3)]
Perimeter = 2(2x + 8)
Perimeter = 4x + 16
Therefore, the perimeter of the rectangular field is (4x + 16) m