Two sides of a triangle measure 34 and 51. Complete the inequality that indicates the possible values of the third side of the triangle using the Triangle Inequality Theorem.(1 point) <x<
85
To find the possible values of the third side of the triangle, we need to apply the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's denote the third side of the triangle as "x".
According to the Triangle Inequality Theorem, we have the following inequality:
34 + 51 > x
Simplifying the above inequality, we get:
85 > x
Hence, the complete inequality that indicates the possible values of the third side of the triangle is:
85 > x
To use the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the two known sides measure 34 and 51. So, the inequality will be:
34 + 51 > x
Simplifying the inequality:
85 > x
Therefore, the completed inequality that indicates the possible values of the third side of the triangle is:
x < 85