A triangle has side lengths of 6 inches, 10 inches, 8 inches. How many triangles are possible?
only one, since
6^2 + 8^2 = 10^2
To determine how many different triangles are possible with the given side lengths, we can use the Triangle Inequality Theorem. According to this theorem, for a triangle with side lengths a, b, and c, the sum of any two side lengths must be greater than the third side length.
In this case, the side lengths of the triangle are 6 inches, 10 inches, and 8 inches. We can check if this triangle is possible by comparing the sum of each pair of side lengths with the remaining side length:
1. 6 + 10 = 16 (which is greater than 8), so the pair (6, 10) is valid.
2. 6 + 8 = 14 (which is less than 10), so the pair (6, 8) is not valid.
3. 10 + 8 = 18 (which is greater than 6), so the pair (10, 8) is valid.
Since each pair of side lengths satisfies the Triangle Inequality Theorem, we can conclude that the given triangle is possible.
Therefore, only one triangle is possible with side lengths of 6 inches, 10 inches, and 8 inches.