Step [tex]1[/tex]
Find the value of x
we know that
TR=RV -------> given problem
in this problem we have
[tex]RV=2x+5\\TR=5x-4[/tex]
so
[tex]2x+5=5x-4\\ 5x-2x=5+4\\3x=9\\x=9/3\\x=3\ units[/tex]
Step [tex]2[/tex]
In the right triangle TRS
Find the length of the side RS
we know that
Applying the Pythagorean Theorem
[tex]TS^{2} =TR^{2}+RS^{2}\\RS^{2}=TS^{2} -TR^{2}[/tex]
in this problem we have
[tex]TS=6x-3\\TR=5x-4[/tex]
Substitute the value of x
[tex]TS=6*3-3=15\ units\\TR=5*3-4=11\ units[/tex]
[tex]RS^{2}=(15)^{2} -(11)^{2}\\RS^{2}=104\ units^2[/tex]
Step [tex]3[/tex]
In the right triangle RSV
Find the length of the side VS
Applying the Pythagorean Theorem
[tex]VS^{2} =RV^{2}+RS^{2}[/tex]
in this problem we have
[tex]RV=2x+5=2*3+5=11\ units\\RS^{2}=104\ units^2[/tex]
Substitute in the formula
[tex]VS^{2} =11^{2}+104[/tex]
[tex]VS^{2}=225\ units^2[/tex]
[tex]VS=15\ units[/tex]
therefore
the answer is the option D
the value of the side VS is [tex]15\ units[/tex]
