Given that RS = 20 and QR = 5, identify the length of PS.

Question

 

 

 

 

 

 

 

 

 

 

 

Options:

 

PS = 5

PS = 10

 

Answer 1

you got 3 right angled triangles: PRQ, PRS and PQS. you can right the equations for each as follows:

QR^2+PR^2 = PQ^2       (1)

PR^2+RS^2 = PS^2       (2)

PQ^2+PS^2=(QR+RS)^2 --> PQ^2+PS^2=QR^2+RS^2+2*QR*RS

QR = 5, RS = 20 so PQ^2+PS^2 = 625 (3)

Adding (1) and (2):

QR^2+PR^2+PR^2+RS^2=PQ^2+PS^2       from (3)     QR^2+PR^2+PR^2+RS^2=625 --> 25+2*PR^2+400 = 625

PR = 10

(2) 10^2+20^2 = PS^2--> Ps^2 = 500 so PS = 10*sqrt(5)