Final answer:
Yes, a triangle can have sides with lengths 1ft, 6ft, and 8ft. The triangle inequality theorem confirms that these lengths can form a valid triangle.
Step-by-step explanation:
Yes, a triangle can have sides with lengths 1ft, 6ft, and 8ft. To determine if these lengths can form a valid triangle, we need to check the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the length of the third side.
In this case, we add the lengths of the two smaller sides: 1ft + 6ft = 7ft. Since 7ft is greater than the length of the longest side, 8ft, the triangle inequality is satisfied. Therefore, a triangle with side lengths 1ft, 6ft, and 8ft can exist.
A triangle cannot have sides with lengths 1ft, 6ft, and 8ft because it violates 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. In this case, 1ft + 6ft = 7ft, which is not greater than 8ft. Therefore, a triangle with these side lengths is not possible.