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Kendra Navarro
Mathematics
22 November, 06:57
If RX = 4 and XS = 9, then XT = 6 6.5 √13 18
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Jon Frazier
22 November, 07:16
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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
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