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)

Question

Responses

4.4<x<80.73
4.4 less than x less than 80.73

4.04<x<80.1
4.04 less than x less than 80.1

4.67<x<42.3
4.67 less than x less than 42.3

4.67<x<80.73

Answer 1

To find the range of values for the third side \( x \) of a triangle when the other two sides measure 42.7 mm and 38.03 mm, we can use the triangle inequality theorem. The theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.

This gives us three inequalities to consider:

1. \( 42.7 + 38.03 > x \)
2. \( 42.7 + x > 38.03 \)
3. \( 38.03 + x > 42.7 \)

Let's calculate these one by one.

1. From \( 42.7 + 38.03 > x \): \[ 80.73 > x \quad \text{or} \quad x < 80.73 \]

2. From \( 42.7 + x > 38.03 \): \[ x > 38.03 - 42.7 \ x > -4.67 \quad \text{(This does not affect the lower limit since x must be positive)} \]

3. From \( 38.03 + x > 42.7 \): \[ x > 42.7 - 38.03 \ x > 4.67 \]

Now combining the results we get: \[ 4.67 < x < 80.73 \]

Based on the answers provided, the correct choice is: 4.67 < x < 80.73.