Answer: To determine the possible length of the third side of the triangular pen, we need to apply the triangle inequality theorem. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let x be the length of the third side.
For a triangle with sides 14 feet, 10 feet, and x feet:
Sum of the first two sides > Length of the third side:
14 + 10 > x
24 > x
Sum of the first side and the third side > Length of the second side:
14 + x > 10
x > -4
Sum of the second side and the third side > Length of the first side:
10 + x > 14
x > 4
Based on the inequality conditions, the possible range for the length of the third side (x) is:
4 < x < 24
So, any value of x that falls within this range could be the length of the third side of the triangular pen. Among the given options, x = 21 feet and x = 28 feet are within this range, so either of these lengths could be the length of the third side. However, x = 35 feet and x = 37 feet are outside the range and, therefore, cannot be the length of the third side for this particular triangular pen.