You’re a farmer and want to build an enclosure shaped like an isosceles triangle where the
sides are twice as long as the base. If you own 500 feet of fencing, what are the possible
sizes for the base? You need not use all the fencing and decimal lengths are OK. Remember
the real-world nature of this problem, and also draw your solution set on the number line.

The number line above represents the possible sizes for the base \( b \) of the triangular enclosure, showing that \( b \) can range from just above 0 feet to a maximum of 100 feet.

Would you like further details, or do you have any questions?

### Related Questions
1. How does changing the shape (e.g., to a rectangle) affect the possible base size?
2. How would a different total fencing length change the maximum base length?
3. What area would the enclosure cover if the base is set at 100 feet?
4. How would using all 500 feet of fencing alter the size and shape?
5. Could you build multiple smaller triangles with the fencing, and how?

### Tip
When designing enclosures, consider both the perimeter for fencing and the area inside to maximize usable space.

You’re a farmer and want to build an enclosure shaped like an isosceles triangle where the sides are twice as long as the base. If you own 500 feet of fencing, what are the possible sizes for the base? You need not use all the fencing and decimal lengths are OK. Remember the real-world nature of this problem, and also draw your solution set on the number line.

Explore how to determine possible base sizes for an isosceles triangle enclosure given a 500-foot fencing limit. This problem covers essential geometry concepts, such as triangle perimeter and the Triangle Inequality Theorem. Ideal for students in Grades 9-10.

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