Question

question 7 (1 point) can the sides of a triangle have lengths 5.2, 2.6, and 5.77 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:

1. \(a + b>c\)
2. \(a + c>b\)
3. \(b + c>a\)

Step2: Identify the side lengths

Let \(a = 5.2\), \(b = 2.6\), and \(c = 5.77\).

Step3: Check the first inequality (\(a + b>c\))

Calculate \(a + b\): \(5.2+2.6 = 7.8\). Now, compare \(7.8\) with \(c = 5.77\). Since \(7.8>5.77\), this inequality holds.

Step4: Check the second inequality (\(a + c>b\))

Calculate \(a + c\): \(5.2 + 5.77=10.97\). Compare \(10.97\) with \(b = 2.6\). Since \(10.97>2.6\), this inequality holds.

Step5: Check the third inequality (\(b + c>a\))

Calculate \(b + c\): \(2.6+5.77 = 8.37\). Compare \(8.37\) with \(a = 5.2\). Since \(8.37>5.2\), this inequality holds.

Since all three triangle inequalities are satisfied, the three lengths can form a triangle.

Answer:

A. yes