Given,
LP = 15, PR = 9
Point P lies on the line segment PR. It would mean that,
LP + PR = LR
⇒LR = 15 + 9
⇒ LR = 24
Hence, "LR = 24 because LP + PR = LR according to the Segment Addition Postulate, and 15 + 9 = 24 using substitution" is the correct option.
The measure of ? is 36, because if the perimeter of the triangle is 96 and there are 3 sides subtract the base length of 24 from 96 getting you 72 and divide 72 by 2 getting you 36 because there are 2 other sides that are the same length.
1 is the answer I am sure of it.
