Question

sides of a triangle quick check
find the range of values for the third side of a triangle if two of its sides measure 42.7 mm and 38.03 mm. (1 point)
○ ( 4.67 < x < 80.73 )
○ ( 4.4 < x < 80.73 )
○ ( 4.04 < x < 80.1 )
○ ( 4.67 < x < 42.3 )

Explanation:

Step1: Recall triangle inequality theorem

For a triangle with sides \(a\), \(b\), and \(c\), the triangle inequality theorem states that the length of any side must be greater than the absolute difference of the other two sides and less than the sum of the other two sides. So, if two sides are \(a = 42.7\) mm and \(b=38.03\) mm, and the third side is \(x\), then \(|a - b| < x < a + b\).

Step2: Calculate the difference

First, calculate \(|42.7 - 38.03|\).
\(42.7-38.03 = 4.67\), so \(|42.7 - 38.03|= 4.67\).

Step3: Calculate the sum

Next, calculate \(42.7+38.03\).
\(42.7 + 38.03=80.73\).

Step4: Determine the range

From the triangle inequality theorem, we have \(4.67 < x < 80.73\).

Answer:

\(4.67 < x < 80.73\) (the first option: \(4.67 < x < 80.73\))