Answer:
[tex]RU=11[/tex]
Step-by-step explanation:
We have been an image of triangle RST. We are asked to find the measure of median RU.
We know that median of a triangle divides opposite side of triangle into two equal parts.
We can see that side ST is the opposite side of vertex R.
Since we have been given that RU is median of triangle, so TU is equal to SU.
[tex]TU=SU[/tex]
[tex]7x-6=4x[/tex]
Upon subtracting 7x from both sides of our equation, we will get:
[tex]7x-7x-6=4x-7x[/tex]
[tex]-6=-3x[/tex]
[tex]\frac{-6}{-3}=\frac{-3x}{-3}[/tex]
[tex]2=x[/tex]
Now, we will substitute [tex]x=2[/tex] in the expression for RU, we will get:
[tex]RU=3x+5[/tex]
[tex]RU=3(2)+5[/tex]
[tex]RU=6+5[/tex]
[tex]RU=11[/tex]
Therefore, the length of RU is 11 units.
