Question

Determine which set of side measurements could be used to form a triangle.

12, 23, 7
10, 7, 2
O8, 3, 11
5, 11, 8

Answer 1

A set of side measurements can be used to form a triangle if and only if the sum of the lengths of any two sides is greater than the length of the third side. This is known as the Triangle Inequality Theorem.

Let's apply this theorem to each set of side measurements:

1. 12, 23, 7: Not a valid triangle, because (12 + 7) is not greater than 23.

2. 10, 7, 2: Not a valid triangle, because (2 + 7) is not greater than 10.

3. 8, 3, 11: Not a valid triangle, because (3 + 8) is not greater than 11.

4. 5, 11, 8: This set of side measurements can form a triangle, because (5 + 8) is greater than 11, (5 + 11) is greater than 8, and (8 + 11) is greater than 5.

So, the only set of side measurements that can form a triangle is 5, 11, 8.