Mrs. Barto has a pet rabbit and wants to build a pen for it. She has 3 pieces of lumber: one is 3 ft, one is 7 ft, and the other is 8 ft long. Can she build a closed triangular pen with these three boards (will the boards form a triangle)?

Yes, it is possible

Step-by-step explanation:

In a triangle, the length of the longest side of the triangle cannot be larger than the sum of the lenghts of the two shortest sides.

In formula, this means that:

where

c is the length of the longest side

a, b are the lengths of the shortest side

In this problem, we want to build a triangle using 3 pieces of lumber, each of length:

a = 3 ft

b = 7 ft

c = 8 ft

We can verify that the length of the longest piece of lumber is less than the sum of the lengths of the other two sides, so:

Therefore, yes, it is possible to build a closed triangular pen.