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

Answer 1

PQ^2+PR^2=QR^2 and PS^2+PQ^2+QS^2 and PS^2+PR^2=SR^2,
adding 2nd and third eq, and substituting PR^2 and PQ^2 we get QS*SR=144.
hence answer is QS=6 and SR=24