Answer:
Option B. x = 10
Step-by-step explanation:
If TV ║ QS then triangles RTV and ΔRQS will be similar.
By the theorem of similarity corresponding sides should be in the same ratio.
Therefore, [tex]\frac{RT}{RV}=\frac{RQ}{RS}[/tex]
[tex]\frac{(x + 4)}{(x -3)+(x + 4)}=\frac{(x+10)}{x+(x+10)}[/tex]
[tex]\frac{x+4}{2x+1}=\frac{x+10}{2x+10}[/tex]
By cross multiplication
(x + 4)(2x + 10) = (x + 10)(2x + 1)
2x² + 10x + 8x + 40 = 2x² + x + 20x + 10
18x + 40 = 21x + 10
21x - 18x = 40 - 10
3x = 30
x = 10
Option C. x = 10 is the answer.
