1) The length of the side RS is 24 units. 2) The value of [tex]x[/tex] is 5.5 units. 3) The value of [tex]y[/tex] is 5.3 units. 4) The length of side UW is 11 units. 5) The length of side UV is 15.9 units.
Given information:
In triangle RST, U is the mid-point of side SR, V is the mid-point of the side ST and W is the mid-point of the side RT.
So, the length of the sides can be written as,
[tex]SU=UR=\dfrac{1}{2}SR\\SV=VT=\dfrac{1}{2}ST\\RW=WT=\dfrac{1}{2}RT[/tex]
It is also given that:
[tex]UR=12\\RW=15.9\\WT=3y\\VT=11\\SV=2x[/tex]
1). Now, the length of side SR will be,
[tex]RS=2UR\\RS=2\times12\\RS=24[/tex]
The length of the side RS is 24 units.
2). To find the value of [tex]x[/tex], use the relation between SV and VT as,
[tex]SV=VT\\2x=11\\x=\dfrac{11}{2}\\x=5.5[/tex]
The value of [tex]x[/tex] is 5.5 units.
3). To find the value of [tex]x[/tex], use the relation between RW and WR as,
[tex]WT=RW\\3y=15.9\\y=5.3[/tex]
The value of [tex]y[/tex] is 5.3 units.
Now, the mid-point theorem states that "a line segment joining the mid-points of two sides of a triangle is parallel to the third side and its length is equal to half of the third side".
4). Use the mid-point theorem to get the value of side UW as,
[tex]UW=\dfrac{1}{2}ST\\UW=\dfrac{1}{2}\times 2VT\\UW=VT=11[/tex]
Thus, the length of side UW is 11 units.
5). Use the mid-point theorem to get the value of side UV as,
[tex]UV=\dfrac{1}{2}RT\\UV=\dfrac{1}{2}\times RW\\UV=RW=15.9[/tex]
Thus, the length of side UV is 15.9 units.
For more details, refer to the link:
https://brainly.com/question/13677972
