Answer: THe correct option is (C) 15.
Step-by-step explanation: We are given to find the length of SR in the right-angled triangle SRQ as shown in the figure.
Since RT is perpendicular to the hypotenuse SQ, so triangle RTQ and SRT are also right-angled triangles at angle RTQ and RTS respectively.
Also, RQ = 20 units and TQ = 16 units.
Using Pythagoras theorem in triangle RTQ, we have
[tex]RQ^2=RT^2+TQ^2\\\\\Rightarrow RT=\sqrt{RQ^2-TQ^2}\\\\\Rightarrow RT=\sqrt{20^2-16^2}\\\\\Rightarrow RT=\sqrt{144}\\\\\Rightarrow RT=12.[/tex]
Now, since RT is perpendicular to the hypotenuse of ΔRST, so we get
[tex]ST\times TQ=RT^2\\\\\Rightarrow RS\times 16=144\\\\\Rightarrow RS=\dfrac{144}{16}\\\\\Rightarrow RS=9.[/tex]
Again, using Pythagoras theorem in right-angled triangle RST, we get
[tex]SR^2=RT^2+ST^2\\\\\Rightarrow SR=\sqrt{144+81}\\\\\Rightarrow SR=\sqrt{225}\\\\\Rightarrow SR=15.[/tex]
Thus, the length of SR is 15 units.
Option (C) is CORRECT.
