Question

question 3
1 pts
two sides of a triangle measure 12 and 13 inches. between what two measures can the third side be?
between and
question 4
1 pts
two sides of a triangle measure 12 and 3 units. between what two measures can the third side be?
< length of third side <

Explanation:

Question 3

Step1: Recall triangle inequality theorem

For a triangle with sides \(a\), \(b\), \(c\), the triangle inequality 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 \(a = 12\) and \(b=13\), then the third side \(c\) satisfies \(|a - b| < c < a + b\).

Step2: Calculate the difference and sum

First, calculate the absolute difference: \(|12 - 13|=| - 1| = 1\). Then, calculate the sum: \(12+13 = 25\). So the third side must be between \(1\) and \(25\) inches.

Step1: Recall triangle inequality theorem

For a triangle with sides \(a\), \(b\), \(c\), the triangle inequality 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 \(a = 12\) and \(b = 3\), then the third side \(c\) satisfies \(|a - b| < c < a + b\).

Step2: Calculate the difference and sum

First, calculate the absolute difference: \(|12 - 3|=9\). Then, calculate the sum: \(12 + 3=15\). So the third side must be between \(9\) and \(15\) units.

Answer:

Between \(1\) and \(25\)

Question 4