Question

In triangle, HIJ, HI = 48, and IJ = 27. What is the range of values for the length third side?

Answer 1

Answer:

The range is between 21 and 75

Step-by-step explanation:

"The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side."

Any two sides of of a triangle added together cannot be equivalent to or less than the length of the third side. Knowing this, we can figure out the range. If you add 48 and 27, you get 75.  We know 75 is the top of the range, the length of the third side cannot be 75 or greater. Going the other way, if you assume that the third side is one of the smaller ones, you can identify 48 as the largest value. If you subtract 27 from 48 you get 21, so the length of the third side cannot be 21 or lower.

This gives us the range. Just keep this rule in mind. Hope this helped!