Mr. Franco is making a triangular cement slab and needs to set boards before he can pour the

cement. He has already set two boards that are 5 feet and 8 feet in length. What is a
reasonable range for the length of the third board that Mr. Franco could set for this triangular
cement slab?

answers-A. The third board needs to be greater than 3 feet in length.
B. The third board can be between 3 feet and 13 feet in length.
C. The third board needs to be less than 13 feet in length.
D. The third board can be 3 feet or 13 feet in length.

B

If two sides are a and b, the third side c must obey

a-b < c < a+b

because any side must be less than the sum of the other two.

To determine the length of the third board for the triangular cement slab, we can use the triangle inequality theorem. According to this theorem, for a triangle to be possible, the sum of the lengths of any two sides of the triangle must be greater than the length of the third side.

In this case, we know that Mr. Franco has already set two boards measuring 5 feet and 8 feet in length. Let's denote the length of the third board as x. Applying the triangle inequality theorem, we can write the following inequalities:

5 + 8 > x
13 > x

This means that the length of the third board must be greater than 3 feet because the minimum value of x (the length of the third board) is 3 (since it cannot be negative). However, there is no maximum constraint on the length of the third board, so it can be any value greater than 3 feet.

Therefore, the reasonable range for the length of the third board is from 3 feet to infinity. In the given answer choices, the option that correctly reflects this range is B. The third board can be between 3 feet and 13 feet in length.