Let's solve the problem step-by-step. We are given the following:
- RT = 8x - 6
- RS = 16
- ST = 2x - 4
We know that RT is the sum of RS and ST:
RT = RS + ST
Substitute the given expressions into this equation:
8x - 6 = 16 + 2x - 4
Now, let's simplify and solve for [tex]\( x \)[/tex]:
8x - 6 = 12 + 2x
To isolate [tex]\( x \)[/tex], we first subtract [tex]\( 2x \)[/tex] from both sides:
8x - 2x - 6 = 12
6x - 6 = 12
Next, we add 6 to both sides to further isolate [tex]\( x \)[/tex]:
6x - 6 + 6 = 12 + 6
6x = 18
Now, we divide by 6:
x = 18 / 6
x = 3
Now that we have the value of [tex]\( x \)[/tex], we can substitute it back into the expressions for RT and ST to find their lengths.
RT = 8x - 6
RT = 8(3) - 6
RT = 24 - 6
RT = 18
Similarly, for ST:
ST = 2x - 4
ST = 2(3) - 4
ST = 6 - 4
ST = 2
So, the lengths are:
- RT = 18
- ST = 2
Thus, using these calculations, we have determined that the length of RT is 18 units and the length of ST is 2 units.
