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

Question

asked Feb 9, 2020 186k views

2 Answers

Gianlucca · Answer 1 · 2020-02-15T18:07:25+0000

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.