Point S is on line segment RT. Given RT = 2x, RS = 3x - 8, and ST = x,
determine the numerical length of ST.
Given that RS = 3x - 8, ST = x, and RT = 2x, we can determine the length of ST.
RT = RS + ST
2x = (3x - 8) + x
2x = 4x - 8
8 = 2x
4 = x
Therefore, the numerical length of ST is 4.
To determine the length of ST, we need to solve for the value of x in the equation ST = x.
We are given that RT = 2x, RS = 3x - 8, and ST = x.
Since point S is on line segment RT, the sum of RS and ST should be equal to RT.
Therefore, RS + ST = RT.
Substituting the given lengths, we get (3x - 8) + x = 2x.
Simplifying the equation, we have 4x - 8 = 2x.
To isolate the x-term, we subtract 2x from both sides, which gives us 2x - 8 = 0.
Adding 8 to both sides gives us 2x = 8.
Finally, dividing both sides by 2, we find that x = 4.
Therefore, the numerical length of ST is equal to x, which is 4.
To find the length of ST, we can use the information given in the problem. We know that RS + ST = RT, so we can set up an equation:
RS + ST = RT
Substituting the given values, we have:
(3x - 8) + x = 2x
Simplifying the equation:
4x - 8 = 2x
Bringing the terms with x on one side, we get:
4x - 2x = 8
2x = 8
Dividing both sides by 2:
x = 4
Now that we have found the value of x, we can substitute it back into the expression for ST to find its length:
ST = x = 4
Therefore, the numerical length of ST is 4.