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 12 inches long.

Which of the following could be the lengths of segments QS and SR?
Answer
QS = 6 inches, SR = 24 inches
QS = 2 inches, SR = 6 inches
QS = 44 inches, SR = 100 inches
QS = 12 inches, SR = 132 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 12 inches long.
 
 
 
Which of the following could be the lengths of segments QS and SR?
Answer
		QS = 6 inches, SR = 24 inches
		QS = 2 inches, SR = 6 inches
		QS = 44 inches, SR = 100 inches
		QS = 12 inches, SR = 132 inches

anonymous · Answer

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directrix · Answer

QS = 6 inches, SR = 24 inches

The product of QS and SR has to be 144 because ..

directrix · Answer

If an altitude is drawn to the hypotenuse of a right triangle, then the length of the altitude is the geometric mean between the lengths of the segments of the hyptenuse.

So, QS/12 = 12/SR

Cross multiplying gives QS * SR = 12*12 = 144. So, just look for two factors that multiply to 144.