The following side lengths, in meters, were given to a carpenter to build a
front porch with a triangular design. The carpenter needs to determine
which set of lengths will make a triangle to be able to use it in his design.
Option 1: Side lengths: 3, 3, 6
Option 2: Side lengths: 6, 8, 10
Option 3: Side lengths: 4, 6, 13(1 point)
To determine if a set of side lengths can form a triangle, we can use the triangle inequality theorem.
According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check each option:
Option 1: Side lengths: 3, 3, 6
In this case, the sum of the two shorter sides (3 + 3 = 6) is equal to the length of the longest side (6). Therefore, this triangle can be formed.
Option 2: Side lengths: 6, 8, 10
In this case, the sum of the two shorter sides (6 + 8 = 14) is greater than the length of the longest side (10). Therefore, this triangle can be formed.
Option 3: Side lengths: 4, 6, 13
In this case, the sum of the two shorter sides (4 + 6 = 10) is less than the length of the longest side (13). Therefore, this triangle cannot be formed.
So, the sets of side lengths that will make a triangle for the carpenter's design are Option 1 (3, 3, 6) and Option 2 (6, 8, 10).