Question

A triangle has two sides of length 3.4 and 7.5. What compound inequality describes the possble lengths for the third side, x? Write a compound inequality like 1

Answer 1

The possible lengths for the third side of the triangle are between 4.1 and 10.9.

Step-by-step explanation:

The lengths of a triangle's sides must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. In this case, the two given sides are 3.4 and 7.5. Let x represent the length of the third side. So, the compound inequality that describes the possible lengths for the third side is:

3.4 + 7.5 > x and x > 7.5 - 3.4

Simplifying the compound inequality gives:

10.9 > x and x > 4.1

Therefore, the possible lengths for the third side, x, are between 4.1 and 10.9.