Answer:
RX=4
Step-by-step explanation:
We are given:
RT = 6 and RS = 9
As RTS is a right angled triangle such that side RS is the hypotenuse of ΔRTS.
Hence on using the Pythagorean theorem we calculate the length of the side TS.
[tex]RS^{2}=RT^2+TS^2\\\\9^2=6^2+TS^2\\\\81=36+TS^2\\\\TS^2=81-36=45\\\\TS=3\sqrt{5}[/tex]
Now again in Right triangle TXS let the length of side SX be 'x'.
Now using Pythagorean Theorem in ΔTXS we have:
[tex]TS^2=TX^2+SX^2\\\\45=TX^2+x^2\\\\TX^2=45-x^2[/tex]
As [tex]RX=RS-SX=9-x[/tex]
Now again using Pythagorean theorem in triangle TXR we have:
[tex]RT^2=RX^2+TX^2\\\\6^2=(9-x)^2+(45-x^2)\\\\36=81+x^2-18x+45-x^2\\\\36=81-18x+45\\\\18x=81+45-36\\\\18x=90\\\\x=5[/tex]
Hence, the length of side RX=9-5=4
RX=4
