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)
• Option 1
• Option 2
• Option 3
To determine if the given sets of side lengths can form a triangle, we need to apply the triangle inequality theorem. According to this 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 lengths of the two equal sides is 3 + 3 = 6, which is equal to the length of the third side. Since the sums are equal, this set of lengths does not satisfy the triangle inequality theorem, and thus, it cannot form a triangle.
Option 2: Side lengths: 6, 8, 10
In this case, the sum of the lengths of the two smaller sides is 6 + 8 = 14, which is greater than the length of the third side (10). This set of lengths satisfies the triangle inequality theorem, and thus, it can form a triangle.
Option 3: Side lengths: 4, 6, 13
In this case, the sum of the lengths of the two smaller sides is 4 + 6 = 10, which is less than the length of the third side (13). This set of lengths does not satisfy the triangle inequality theorem, and thus, it cannot form a triangle.
Based on the analysis above, the set of side lengths that will make a triangle and can be used in the carpenter's design is Option 2: Side lengths: 6, 8, 10.