Question

problem 8: (first taught in lesson 45)
the lengths of two sides of a triangle are given. find the lengths that the third side must be greater than and less than.
a. 7, 2 b. 12, 21
after you enter your answer press go.
a. > 3rd side >
b. > 3rd side >

Explanation:

Step1: Recall triangle side - length rule

For a triangle with side lengths \(a\), \(b\), and \(c\), \(|a - b|\lt c\lt a + b\)

Step2: Solve part a

Given \(a = 7\), \(b = 2\)
\(a + b=7 + 2=9\)
\(|a - b|=|7 - 2| = 5\)

Step3: Solve part b

Given \(a = 12\), \(b = 21\)
\(a + b=12+21 = 33\)
\(|a - b|=|12 - 21|=9\)

Answer:

a. \(9>3\text{rd side}>5\)
b. \(33>3\text{rd side}>9\)