A cow is tethered by a 120-ft rope to the inside corner of an L-shaped building, as shown in the figure. Find the area that the cow can graze. (Let a = 20 ft, b = 60 ft, c = 120 ft, d= 70 ft, and e = 60 ft. Round your answer to the nearest whole number.) ft² d

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A cow is tethered by a 120-ft rope to the inside corner of an L-shaped building, as shown in the figure. Find the area that the cow can graze. (Let \( a = 20 \, \text{ft}, \, b = 60 \, \text{ft}, \, c = 120 \, \text{ft}, \, d = 70 \, \text{ft}, \, \text{and} \, e = 60 \, \text{ft} \). Round your answer to the nearest whole number.)

**Diagram Explanation:**

The image shows an L-shaped building with a cow tethered at the corner by a rope.

- The building shape is represented by two rectangles, forming an "L".
- Dimensions around the building are labeled as follows:
  - \( a = 20 \) ft: The shorter width of the upper rectangle.
  - \( b = 60 \) ft: The longer height of the left rectangle.
  - \( c = 120 \) ft: The length of the rope.
  - \( d = 70 \) ft: One of the sides of the lower rectangle.
  - \( e = 60 \) ft: The other side of the lower rectangle.

The shaded green area represents the region where the cow can graze, forming semicircles and partial circles around the building based on the length of the rope and the L-shaped obstruction.

Input the computed grazing area in the provided blank field labeled "ft²".
Transcribed Image Text:A cow is tethered by a 120-ft rope to the inside corner of an L-shaped building, as shown in the figure. Find the area that the cow can graze. (Let \( a = 20 \, \text{ft}, \, b = 60 \, \text{ft}, \, c = 120 \, \text{ft}, \, d = 70 \, \text{ft}, \, \text{and} \, e = 60 \, \text{ft} \). Round your answer to the nearest whole number.) **Diagram Explanation:** The image shows an L-shaped building with a cow tethered at the corner by a rope. - The building shape is represented by two rectangles, forming an "L". - Dimensions around the building are labeled as follows: - \( a = 20 \) ft: The shorter width of the upper rectangle. - \( b = 60 \) ft: The longer height of the left rectangle. - \( c = 120 \) ft: The length of the rope. - \( d = 70 \) ft: One of the sides of the lower rectangle. - \( e = 60 \) ft: The other side of the lower rectangle. The shaded green area represents the region where the cow can graze, forming semicircles and partial circles around the building based on the length of the rope and the L-shaped obstruction. Input the computed grazing area in the provided blank field labeled "ft²".
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