Question

Points P, Q, R, S are on a straight line such that
PQ = QR = RS. K is a point such that (angle)PKS = 90°, and
KS = RS. If PK^2 = 72, find KS,PS,PR
​

Answer 1

Answer:

SK= 2.6832

PS= 8.0498

PR= 5.3667

Step-by-step explanation:

Let PQ= x

PS=3x

as /_pks= 90 KS is perpendicular to PS

and therfore we can use Pythagoras theorem

PK^2= Ps^2 + SK^2

we know that, pk^2= 72

and SK=RS= x

And PS=PQ+QR+RS= x+x+x=3x

hence,

72= (3x)^2 +x^2

72= 10x^2

x=√7.2 = 2.6832

SK= 2.6832

PS= 3x= 3× 2.6832= 8.0498

PR= PS-RS= 3x-x=2x= 2× 2.6832= 5.3667