Answer – 19 inches
The smallest possible whole-number length of the longest side of an obtuse triangle is the next integer greater than the Pythagorean distance of the other two sides.
Given,
A = 10
B = 15
Pythagoras theorem;
C^2 = A^2 + B^2
C^2 = 15^2 + 10^2
C^2 = 225 + 100
C^2 = 325
C = 18.03
Therefore, the smallest possible whole-number length of the longest side is the next integer greater than 18.03 inches.
The smallest possible whole-number length of the longest side is 19 inches