the leangth of a rectangular field is 30 meter.a fence surrounding the field has a total leangt of 140 meter.what is the leangth of athe diagonal path of this rectangular fieldl
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.
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