The range of possible measurements for the third side is between 1.1 and 6.1, inclusively.
Finding the range of possible measurements of the third side.
Represent the three sides of the triangle as (a), (b), and (c), where (a = 3.7) and (b = 5.2).
The perimeter of the triangle (P) is given by the sum of its three sides:
P = a + b + c
Given that the perimeter is between 10 and 15 inclusively, set up the following inequality:
10 ≤ P ≤ 15
Substitute the expression for (P) into the inequality:
10 ≤ (3.7 + 5.2 + c) ≤ 15
Solve for the range of possible values of (c):
10 ≤ 8.9 + c ≤ 15
Subtract (8.9) from all parts of the inequality:
1.1 ≤ c ≤ 6.1
Therefore, the range of possible measurements for the third side (c) is between (1.1) and (6.1) inclusively.