Answer:
PR = 21
Explanation:
You want the length PR in triangle QRP, which is similar to triangle MNP, given that PM=24, PQ=28, PN+8, and PR=3x-9.
Proportion
Corresponding sides in similar triangles are proportional, so we have ...
PR/PQ = PN/PM
(3x -9)/28 = (x+8)/24 . . . . substitute given values
6(3x -9) = 7(x +8) . . . . . . multiply by 168
18x -54 = 7x +56 . . . . . eliminate parentheses
11x = 110 . . . . . . . . . . . add 54-7x
x = 10 . . . . . . . . . . . . divide by 11
Length
Then the length PR is ...
PR = 3x -9 = 3·10 =9
PR = 21