Question

What is the length of SR ?


9 units
12 units
15 units
18 units

Answer 1

C) - 15 units

Explanation:

Just did the test, good luck :)

Answer 2

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=√(RQ^2-TQ^2)\\\\\Rightarrow RT=√(20^2-16^2)\\\\\Rightarrow RT=√(144)\\\\\Rightarrow RT=12.`

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

`ST* TQ=RT^2\\\\\Rightarrow RS* 16=144\\\\\Rightarrow RS=(144)/(16)\\\\\Rightarrow RS=9.`

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

`SR^2=RT^2+ST^2\\\\\Rightarrow SR=√(144+81)\\\\\Rightarrow SR=√(225)\\\\\Rightarrow SR=15.`

Thus, the length of SR is 15 units.

Option (C) is CORRECT.