What is " the perimeter of a triangle is between 10 and 15 inclusively. if two of the sides of the triangle are 3.7 and 5.2, find the range of possible measurements of the third side."

the range is 1.6 to 6.1

Step by Step:

2 sides of a triangle have to be greater than the third

add 3.7 and 5.2 this gives you 8.9, which means 8.8 is the greatest number that side can be

1.6 is the lowest the side could be because if it was anything lower then 5.2 would be greater than the sum of 3.7 and this side were calculating

that gives you the range 1.6 to 8.8 now we play a little bit of guess a d check trying to make the range fit the last piece of information that we were given that the perimeter is between 10 and 15

the perimeter is the sum of all the sides so pick different numbers from the range we found and play guess and check to find which ones are too high or low in this case the numbers were only to high

the highest number you can have that is within the range we found but fits the perimeter is 6.1

therefore the range 1.6 to 6.1