Question

if two sides of a triangle measure 8 ft and 12 ft, state the range for the third side
cannot be determined
4 < x < 12
8 < x < 20
4 < x < 20

Explanation:

Step1: Recall Triangle Inequality Theorem

The triangle inequality theorem states that the length of any side of a triangle must be greater than the absolute difference of the other two sides and less than the sum of the other two sides. For a triangle with sides \(a\), \(b\), and \(c\), \(|a - b| < c < a + b\).

Step2: Identify the given sides

Here, the two given sides are \(a = 8\) ft and \(b = 12\) ft.

Step3: Calculate the difference and sum

First, find the absolute difference: \(|12 - 8| = 4\). Then, find the sum: \(12 + 8 = 20\).

Step4: Determine the range for the third side

Using the triangle inequality theorem, the length \(x\) of the third side must satisfy \(4 < x < 20\).

Answer:

Green Square Option: \(4 < x < 20\)