Question

A triangle with sides a=8
and c=10
. If side b=3
, would it create a triangle? Enter 1 for “yes” and 2 for “no.”(1 point)

Answer 1

To determine if the three sides \( a = 8 \), \( b = 3 \), and \( c = 10 \) can form a triangle, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.

We need to check the following inequalities:

1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)

Now, substituting the values of \( a \), \( b \), and \( c \):

1. \( 8 + 3 > 10 \) → \( 11 > 10 \) (True)
2. \( 8 + 10 > 3 \) → \( 18 > 3 \) (True)
3. \( 3 + 10 > 8 \) → \( 13 > 8 \) (True)

All three inequalities are satisfied, so the given sides can indeed form a triangle.

The answer is **1** for "yes".