Question

Patrick uses scrap metal to build sculptures. He wants to build a sculpture with triangles. He finds metal rods that are 20 in., 27 in., 47 in., and 67 in. long. Which combinations of three of these lengths can Patrick use to form a triangle? Justify your answer.

Answer 1

Hello !

- for a triangle to be constructible, the longest side must be less than the sum of the other two sides. -

so :

67 smaller than 27+47 ?

67 ⟨ 74 it's the right answer.

I hope I helped you !!

Have a good evening !!!

Answer 2

Patrick can form a triangle using the rod lengths of 20 inches and 27 inches and 47 inches. The other combinations of rod lengths do not meet the conditions laid out by the triangle inequality theorem.

Step-by-step explanation:

The subject of this question is Mathematics, specifically focusing on geometric properties of triangles. According to the triangle inequality theorem, a triangle can only form if the sum of the lengths of the two shorter sides is greater than the length of the longest side. In this context, Patrick uses scrap metal to build sculptures and wants to create triangles from metal rods which are 20 inches, 27 inches, 47 inches, and 67 inches long. Using the triangle inequality theorem, we can determine which combinations of rod lengths can form a triangle:

• If he uses the rod lengths 20 inches, 27 inches, and 47 inches, it would satisfy the theorem since 20+27 = 47. Therefore, these lengths can form a triangle.
• For the rods with lengths of 20 inches, 47 inches, and 67 inches, the sum of the two shorter lengths (20+47 = 67) is not greater than the length of the longest rod (67). Hence, these lengths cannot form a triangle.
• Similarly, for rods measuring 20 inches, 27 inches, and 67 inches, the sum of the two shorter rods (20+27 = 47) is less than the length of the longest rod (67). Therefore, this combination can't form a triangle either.

Learn more about Triangle Inequality Theorem