Frank is constructing a triangular pen for his farm animals. He knows that he needs lengths of 13ft and 25ft. What is a possible length for the third side?

Question

O 10ft
O 11ft
12ft
13ft

Answer 1

To determine a possible length for the third side of the triangle, we can use the triangle inequality theorem, which states that for any triangle with sides of lengths \(a\), \(b\), and \(c\):

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

In this case, we have two sides: \(a = 13\) ft and \(b = 25\) ft. Let's denote the third side as \(c\). We need to find a value for \(c\) that satisfies all three inequalities.

1. Applying the inequalities:

   • From \(a + b > c\): \[ 13 + 25 > c \quad \Rightarrow \quad 38 > c \quad \Rightarrow \quad c < 38 \]

   • From \(a + c > b\): \[ 13 + c > 25 \quad \Rightarrow \quad c > 12 \]

   • From \(b + c > a\): \[ 25 + c > 13 \quad \Rightarrow \quad c > -12 \quad \text{(this condition is always satisfied since } c > 12\text{)} \]

2. Combining the valid inequalities:

   • From the first inequality, \(c < 38\).
   • From the second, \(c > 12\).

This means \(c\) must be greater than 12 and less than 38.

3. Choosing a possible length for \(c\) from the given options:
   • 10 ft (not valid; \(c\) must be > 12)
   • 11 ft (not valid; \(c\) must be > 12)
   • 12 ft (valid since \(c > 12\))
   • 13 ft (valid since \(c > 12\))

Thus, valid options for the length of the third side are 12 ft and 13 ft.

In conclusion, a possible length for the third side is 12 ft or 13 ft.

Answer 2

pick one

Answer 3

I'll choose 12 ft as the possible length for the third side of the triangular pen.