Answer:
[tex] \therefore x =2[/tex]
Step-by-step explanation:
[tex] \triangle TPR \sim \triangle SQR... (given) [/tex]
[tex] \therefore \frac{TP}{SQ} = \frac{PR}{QR}[/tex]
[tex] \therefore \frac{TP}{SQ} = \frac{PQ+QR}{QR}[/tex]
[tex] \therefore \frac{3}{x} = \frac{1\frac{1}{3} +2 \frac{2}{3}}{2 \frac{2}{3}}[/tex]
[tex] \therefore \frac{3}{x} = \frac{\frac{4}{3} + \frac{8}{3}}{\frac{8}{3}}[/tex]
[tex] \therefore \frac{3}{x} = \frac{\frac{12}{3}}{\frac{8}{3}}[/tex]
[tex] \therefore \frac{3}{x} = \frac{12}{8}[/tex]
[tex] \therefore x = \frac{8\times 3}{12}[/tex]
[tex] \therefore x = \frac{24}{12}[/tex]
[tex] \therefore x =2[/tex]
