We are given the following information.
Point S is on the line segment RT.
Length of RT = 43
Length of ST = 51x - 10 (assuming that x must have been omitted due to some mistyping)
Length of RS = 6
Let us draw the situation as per the given information.
As you can see in the above drawing,
RS + ST = RT
Substitute the given values
6 + 51x - 10 = 43
Solve for x
6 + 51x - 10 = 43
51x = 43 + 10 - 6
51x = 47
x = 47/51
Now substitute the value of x into the equation of ST to find the numerical length of ST.
ST = 51(47/51) - 10
ST = 47 - 10
ST = 37
Therefore, the numerical length of ST is 37.
Verification:
RS + ST = RT
6 + 37 = 43
43 = 43
Hence, we got the correct results.
