If RX = 4 and XS = 9, then XT =

RX is + XS is the hypotenuse of the right triangle RTS, then:

(RX + XS)^2 = (RT)^2 + (ST)^2

=> (4+9)^2 = (RT)^2 + (ST)^2

=> 13^2 = (RT)^2 + (ST)^2 equation (1)

Triangle RTX and XST are also right triangles.

RT is the hypotenuse of RTX and ST is the hypotenuse os SXT.

Then, (RT)^2 - (RX)2 = (TX)^2 and (ST)^2 - (SX)^2 = (TX)^2

=> (RT)^2 - (RX)^2 = (ST)^2 - (SX)^2

=> (RT)^2 - (ST)^2 = (RX)^2 -(SX)^2

=> (RT)^2 - (ST)^2 = 4^2 - 9^2 = 16 - 81 = - 65

=> (ST)^2 - (RT)^2 = 65 equation (2)

Now use equations (1) and (2)

13^2 = (RT)^2 + (ST)^2

65 = (ST)^2 - (RT)^2

Add the two equations:

13^2 + 65 = 2(ST)^2

2(ST)^2 =178

(ST)^2 = 234/2 = 117

Now use (ST)^2 - (SX)^2 = (TX)^2

=> (TX)^2 = 117 - 81 = 36

=> (TX) = √36 = 6