Question

Can the lengths 4.6, 3.6, and 7.4 make a triangle?

A) Yes, they can form a triangle.
B) No, they cannot form a triangle.
C) They can form a triangle if one of the lengths is adjusted.
D) They can form a triangle if the sum of two of the lengths is adjusted.

Answer 1

After checking the conditions of the Triangle Inequality Theorem, we confirm that the lengths 4.6, 3.6, and 7.4 can indeed form a triangle because the sum of any two given lengths is greater than the third length.

Step-by-step explanation:

The student asked if the lengths 4.6, 3.6, and 7.4 can make a triangle. To determine whether three lengths can form a triangle, we can use the Triangle Inequality Theorem, which states that 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, we check:

• 4.6 + 3.6 > 7.4
• 4.6 + 7.4 > 3.6
• 3.6 + 7.4 > 4.6

All of these conditions must be true for the lengths to make a triangle. After adding each pair, we see:

• 4.6 + 3.6 = 8.2, which is greater than 7.4
• 4.6 + 7.4 = 12, which is greater than 3.6
• 3.6 + 7.4 = 11, which is greater than 4.6

Since all three conditions are satisfied, the answer to the student's question is A) Yes, they can form a triangle.