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 4 inches long.

Which of the following could be the lengths of segments QS and SR?

QS = 2 inches, SR = 8 inches

QS = 6 inches, SR = 10 inches

QS = 2 inches, SR = 2 inches

QS = 4 inches, SR = 12 inches

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 4 inches long. 
  
Which of the following could be the lengths of segments QS and SR?

 QS = 2 inches, SR = 8 inches

 QS = 6 inches, SR = 10 inches

 QS = 2 inches, SR = 2 inches

 QS = 4 inches, SR = 12 inches

lucaz · Answer

where is the figure?

anonymous · Answer

attachment

anonymous · Answer

here, sorry

lucaz · Answer

QS is already given right? 12ft?

anonymous · Answer

yea

lucaz · Answer

they are similar triangles, so you can find QT aplying pythagorean theorem, then by proportions you can find RT, and use pythagorean theorem again to find SR

lucaz · Answer

but I'm a bit confused, PS is given in inches, is that correct? the answers are also in inches

anonymous · Answer

QS is given 12ft right ..?  but none of ur options have that QS value .?

anonymous · Answer

$$SR=3\sqrt{5} ft. and QS=12ft.$$