18. Dominic built a dog pen with a perimeter of 72 feet (ft). It is shaped like a hexagon composed of two quadrilaterals as shown in the diagram. Side g of the dog pen is a gate. What is the length, in feet, of the gate?
Answer: D
The length of the gate is 12 feet.
The gate, represented as side g of the hexagonal dog pen, measures 12 feet in length based on the given perimeter of 72 feet.
A) 10
Option A is incorrect as it suggests that the gate measures 10 feet. Given the total perimeter of the hexagon is 72 feet, and considering the geometry of the shape, 10 feet would not align with the lengths of the other sides and the requirement to maintain the total perimeter.
B) 5
Option B is also incorrect. A gate measuring 5 feet would be too short to satisfy the conditions of the hexagonal pen's perimeter, as it would not leave enough length for the other sides to maintain the necessary total of 72 feet.
C) 8
Option C is incorrect because a length of 8 feet for the gate would not fulfill the perimeter requirement. If side g were 8 feet, the remaining lengths would not be able to sum up to the total perimeter of 72 feet, making this choice invalid.
D) 12
Option D is correct, as it accurately represents the length of the gate. A gate of 12 feet allows the remaining sides of the hexagonal pen to combine properly and reach the total perimeter of 72 feet, adhering to the geometric constraints of the shape.
Conclusion
The correct answer is 12 feet, as it is the only option that fits within the geometric requirements of the hexagonal dog pen's perimeter. All other options fail to maintain the total perimeter of 72 feet, demonstrating that they cannot be the correct length for the gate.