Question

1. given a triangle with sides 7, 20, x. what is the range of possible values for the third side? select would x = 17 be a possible answer? select would x = 35 be a possible answer? select would x = 12 be a possible answer? select

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. So, \(|a - b|\lt c\lt a + b\), where \(a = 7\) and \(b = 20\).

Step2: Calculate the lower - bound

\(20−7=13\).

Step3: Calculate the upper - bound

\(20 + 7=27\). So, \(13\lt x\lt27\).

Step4: Check \(x = 17\)

Since \(13\lt17\lt27\), \(x = 17\) is a possible value.

Step5: Check \(x = 35\)

Since \(35>27\), \(x = 35\) is not a possible value.

Step6: Check \(x = 12\)

Since \(12<13\), \(x = 12\) is not a possible value.

Answer:

Range of \(x\): \(13\lt x\lt27\)
Is \(x = 17\) possible? Yes
Is \(x = 35\) possible? No
Is \(x = 12\) possible? No