Question

question 8 of 10
a triangle has two sides of lengths 8 and 10. what value could the length of the third side be? check all that apply.
a. 4
b. 8
c. 7
d. 18
e. 10
f. 20

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let the sides of the triangle be \(a = 8\), \(b = 10\), and \(c\) be the third - side. Then \(a + b>c\), \(a + c>b\), and \(b + c>a\). Also, \(|a - b|<c<(a + b)\).

Step2: Calculate the range of the third - side

We have \(|8 - 10|=2\) and \(8 + 10 = 18\). So, \(2

Answer:

A. 4
B. 8
C. 7
E. 10