Question

Jeremiah uses bamboo rods to make the frame of a tailless kite. He ties three bamboo rods together to form a right triangle PQR. He then ties another rod from P that meets RQ at a right angle. Segment PS in the figure below represents this rod and it is 6 inches long.
http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_0309_17/image0014e247e87.jpg
Which of the following could be the lengths of segments QS and SR?

QS = 4 inches, SR = 9 inches

QS = 6 inches, SR = 30 inches

QS = 2 inches, SR = 3 inches

QS = 16 inches, SR = 20 inches


I think the

Answer 1

*answer is a?

Answer 2

How did you approach the problem?

Answer 3

Well...I'm not sure. My brain is slightly discombobulated but it made sense in my own little world

Answer 4

I'll explain you:)

Answer 5

question doesn't have much info, so we need to check each of the options

Answer 6

In all the options we have QS and SR
triangle PQS is a right triangle
use Pythagoras and find PQ ( you have QS and PS)
then in triangle PSR
find PR using Pythagoras ( you have PS and SR)
you have now PQ, PR and QR (=QS+SR)
these sides make the right triangle PQR
here you verify if Pythagoras is satisfied
\[QR^2=PR^2+PQ^2\]
If it's satisfied then that option is correct
@rebeccaskell94

Answer 7

Do you get this?

Answer 8

well I know PS is 6^2 but you don't have that as an option :/ so idunnow

Answer 9

@rebeccaskell94 I'll check first option for you

Answer 10

Oh! I understand your point! okay hold on give me a sec and I'll try it! The process of elimination. I'm a retard

Answer 11

take your time, it happens when you don't sleep enough :P

Answer 12

oh wait. Okay, maybe not. I'm still confused.

Answer 13

QS=4 , SR=9
triangle PQS is a right triangle
use Pythagoras and find PQ
\[PQ^2=QS^2+SR^2\]\[PQ^2=4^2+9^2=97\]
so
\[\large PQ=\sqrt {97}\]
now
triangle PSR
we'll find PR using Pythagoras ( we have PS and SR)
PS=6
SR=9
\[PR^2=PS^2+SR^2\]
\[ PR^2=6^2+9^2=117\]

so
\[\large PR=\sqrt{117}\]
now in triangle PQR
\[QR^2=PQ^2+PR^2\]
this is the verification part
\[QR=QS+SR=13\]
\[13^2=(\sqrt{117})^2+(\sqrt{97})^2\]
\[169\ne 117+97\]
so option a is not our answer, now you need to check the other 3 following the same procedure

Answer 14

soo much D:

alright

6^2 + 6^2 = 72
PQ = √72

so far. is that good?

Answer 15

sorry,
In triangle PQS
\[PQ^2=QS^2+PS^2\]
QS=4 PS=6
\[PQ^2=16+36=>PQ=\sqrt {52}\]
option a is our answer
\[169= 52+117\]
OMG I did blunt mistake

Answer 16

I WAS RIGHT :D ?!

Answer 17

Yeah :D

Answer 18

YESSSSSSSs

Answer 19

Did you understand?
I think you did understand, you were using correct sides for PQ
@rebeccaskell94 good work

Answer 20

Thank you :D Yes