Question

question 6 (1 point) can the sides of a triangle have lengths 1, 6, and 7? yes no

Explanation:

Step1: Recall Triangle Inequality Theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the sum of the lengths of any two sides must be greater than the length of the remaining side. Mathematically, this means:
\(a + b>c\), \(a + c>b\), and \(b + c>a\)

Step2: Check the given side lengths

Let \(a = 1\), \(b = 6\), and \(c = 7\)

• Check \(a + b>c\): \(1+6 = 7\), but \(7\) is not greater than \(7\) (it is equal).
• Since one of the triangle inequalities is not satisfied (the sum is equal, not greater), the three lengths cannot form a triangle.

Answer:

b. No