Question

What is the length of SR ? 9 units 12 units 15 units 18 units

Answer 1

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

$RQ^2=RT^2+TQ^2\\\\\Rightarrow RT=\sqrt{RQ^2-TQ^2}\\\\\Rightarrow RT=\sqrt{20^2-16^2}\\\\\Rightarrow RT=\sqrt{144}\\\\\Rightarrow RT=12.$

Now, since RT is perpendicular to the hypotenuse of ΔRST, so we get

$ST\times TQ=RT^2\\\\\Rightarrow RS\times 16=144\\\\\Rightarrow RS=\dfrac{144}{16}\\\\\Rightarrow RS=9.$

Again, using Pythagoras theorem in right-angled triangle RST, we get

$SR^2=RT^2+ST^2\\\\\Rightarrow SR=\sqrt{144+81}\\\\\Rightarrow SR=\sqrt{225}\\\\\Rightarrow SR=15.$

Thus, the length of SR is 15 units.

Option (C) is CORRECT.