In the diagram the length of segment TR can be represented by 5x-4. What is the length os VS? A) 3 unitsB) 11 unitsC) 13 units D) 15 units

Step [tex]1[/tex]Find the value of xwe know thatTR=RV -------> given problemin 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 TRSFind the length of the side RSwe know thatApplying 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 RSVFind the length of the side VSApplying 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]thereforethe answer is the option Dthe value of the side VS is [tex]15\ units[/tex]