Question

Two sides of a triangle have the length of 19 in and 37 in. What is the possible range for the 3rd side?

a) 18 < x < 56
b) 18 ≤ x ≤ 56
c) x > 18
d) x ≥ 56

Answer 1

The possible range for the third side of a triangle with sides measuring 19 in and 37 in is 18 < x < 56.

Step-by-step explanation:

The possible range for the third side of a triangle with sides measuring 19 in and 37 in is 18 < x < 56.

To determine this range, we use 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. In this case, the sum of the two given sides (19 + 37) is 56, so the third side must be longer than 56 - the longest given side (37), which gives us 19. Similarly, the third side must be shorter than the sum of the two given sides (19 + 37), which is 56. Therefore, the range for the third side is 18 < x < 56.