Answer: The required values are
x = 12 units, ST = 60 units and SU = 120 units.
Step-by-step explanation: Given that T is the midpoint of SU, where
ST = 5x and TU = 3x + 24.
We are to find the values of x, ST and SU.
Since T is the midpoint of SU, so we get
[tex]ST=TU\\\\\Rightarrow 5x=3x+24\\\\\Rightarrow 5x-3x=24\\\\\Rightarrow 2x=24\\\\\Rightarrow x=\dfrac{24}{2}\\\\\Rightarrow x=12.[/tex]
So, the value of x is 12.
Therefore,
[tex]ST=5\times12=60[/tex]
and
[tex]SU=5x+3x+24=8x+24=8\times12+24=96+24=120.[/tex]
Thus, the required values are
x = 12 units, ST = 60 units and SU = 120 units.
If T is the Midpoint of line SU the the values of x, ST and SU are;
x= 12
ST= 60
SU= 120
Where; [tex]((x_{1} ,y_{1}), (x_{2},y_{2})[/tex] are co-ordinates of the endpoints of the line.
Therefore;
In this case;
If T is the mid-point of SU then;
ST is equal to TU
But; ST = [tex]5x[/tex] and TU = [tex]3x+24[/tex]
Hence;
[tex]5x =3x+24[/tex]
Putting like terms together
[tex]5x-3x = 24[/tex]
[tex]2x =24[/tex]
Dividing both sides by 2
[tex]x = 12[/tex]
Therefore;
[tex]x = 12[/tex]
But;
[tex]ST = 5x[/tex]
[tex]= 5(12)[/tex]
[tex]= 60[/tex]
[tex]TU = 3x + 24[/tex]
[tex]= 3(12)+ 24[/tex]
[tex]= 36 + 24[/tex]
[tex]= 60[/tex]
Therefore;
ST = TU and
SU = 120 units
Keywords: Mid-point,formula for mid point
Midpoint; https://brainly.com/question/12526212
Example on midpoint: https://brainly.com/question/12526212
Level; High school
Subject: Mathematics
Topic: Vectors
Sub-topic: Midpoint
