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?
The length of the gate is 12 feet.
To determine the length of side g, the gate, we can analyze the perimeter of the hexagonal dog pen, which is composed of two quadrilaterals. Given the total perimeter of 72 feet and the other sides of the pen, we can calculate the length of side g.
If side g were 10 feet, the remaining sides would need to total 62 feet. This would require the other five sides to average 12.4 feet each, which is not feasible given the typical dimensions of a dog pen. Therefore, this option is inconsistent with the perimeter requirement.
Choosing 5 feet for side g would leave 67 feet for the other five sides, leading to an average of 13.4 feet per side. Such a dimension is impractically large for a dog pen design, indicating that this option cannot satisfy the perimeter condition.
If side g were 8 feet, this would result in 64 feet remaining for the other sides. The average length of the other five sides would then be 12.8 feet, which is still unusually large for a typical dog pen configuration, making this option also unworkable.
Selecting 12 feet for side g leaves 60 feet for the remaining five sides. This results in an average length of 12 feet per side, which is a feasible and reasonable dimension for a dog pen, making this choice the only one that meets the perimeter requirement.
In conclusion, the length of the gate side g in Dominic's dog pen must be 12 feet to ensure that the total perimeter of the hexagonal structure equals 72 feet. The other choices fail to provide practical solutions that satisfy the perimeter constraint, reinforcing that 12 feet is the only logical length for the gate.
Related Questions
View allThe number line below shows the solution set of an inequality: Which t...
A bag of dog food weighs 40 pounds. The amount of food in the bag is m...
Which expression is undefined over the real numbers?
Laura walks every evening on the edges of a sports field near her hous...
Simplify: (3x - 5) + (-7x + 2)
Related Quizzes
View allGED Mathematical Reasoning
GED Mathematical Reasoning Answers
GED Reasoning Through Language Arts
GED Reasoning Through Language Arts Practice Test
GED Science Sample Test
GED Science Test Prep
Sample GED Social Studies Test
Social Studies GED Test
- ✓ 500+ Practice Questions
- ✓ Detailed Explanations
- ✓ Progress Analytics
- ✓ Exam Simulations