Question

question 4 (1 point) can the sides of a triangle have lengths 1, 10, and 10? yes no a yes b 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 inequalities for the given sides

Let \(a = 1\), \(b = 10\), and \(c = 10\).

• Check \(a + b>c\): \(1+10 = 11\), and \(11>10\) (true)
• Check \(a + c>b\): \(1 + 10=11\), and \(11>10\) (true)
• Check \(b + c>a\): \(10+10 = 20\), and \(20>1\) (true)

Since all three triangle inequalities are satisfied, a triangle with side lengths 1, 10, and 10 can exist.

Answer:

a. Yes