To find the length of the diagonal path of a rectangular field, we can use the Pythagorean theorem. Let's denote the length of the rectangular field as "L" and the width as "W."

Given: Length of the rectangular field (L) = 30 meters Perimeter of the fence = 140 meters

The perimeter of a rectangle is given by the formula: Perimeter = 2(L + W).

We're given that the perimeter is 140 meters:

140 = 2(L + W)

Now, we can solve for W:

2(L + W) = 140

L + W = 140/2

L + W = 70

We know that L is 30 meters, so we can find W:

30 + W = 70

Subtract 30 from both sides:

W = 70 - 30

W = 40 meters

Now that we have the length (L = 30 meters) and the width (W = 40 meters), we can use the Pythagorean theorem to find the length of the diagonal path (D):

D² = L² + W²

D² = (30²) + (40²)

D² = 900 + 1600

D² = 2500

Now, take the square root of both sides to find D:

D = √2500

D = 50 meters

So, the length of the diagonal path of the rectangular field is 50 meters.