If RX = 4 and XS = 9, then XT = 6 6.5 √13 18

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

Answer: 6