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 10 inches long.

A right triangle PQR with right angle at P. PS meets RQ at a right angle and is 10 inches long.

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

QS = 5 inches, SR = 20 inches

QS = 30 inches, SR = 70 inches

QS = 10 inches, SR = 90 inches

QS = 2 inches, SR = 5 inches

Answer 1

please help

Answer 2

Since they give you QS for all the options, by Pythagoras you can solve for QP since there is a right angle. The valid SR can be determined by using the Pythagorean theorem again, or use common knowledge that the hypotenuse is the longest side of a right triangle