Question

For a construction project, don is making triangular supports out of pieces of wood. which of the following lengths of wood will not produce a triangular support?

a) 5ft, 1 ft, 4 ft
b) 7 ft, 5 ft, 7 ft
c) 15 ft, 16 ft, 17 ft
d) 11 ft, 12 ft, 13 ft

Answer 1

The lengths that will not produce a triangular support according to the Triangle Inequality Theorem are 5ft, 1ft, and 4ft since their sum is not greater than the length of the longest side.

Step-by-step explanation:

For a set of three lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the Triangle Inequality Theorem. Let's apply this theorem to the options given:

• Option A: 5ft, 1ft, 4ft - The sum of the two smaller sides (5ft and 1ft) is 6ft, which is not greater than the longest side (4ft), so these lengths cannot form a triangle.
• Option B: 7 ft, 5 ft, 7 ft - The sum of the two smaller sides (5ft and 7ft) is 12ft, which is greater than the other 7ft side, so these lengths can form a triangle.
• Option C: 15 ft, 16 ft, 17 ft - The sum of any two sides of this set is greater than the third, so these lengths can form a triangle.
• Option D: 11 ft, 12 ft, 13 ft - Similar to option C, the sum of any two sides is greater than the third side, so these lengths can form a triangle.

Therefore, the lengths that will not produce a triangular support are 5ft, 1ft, and 4ft as given in Option A.