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?
Answer







QS = 6 inches, SR = 10 inches








QS = 4 inches, SR = 12 inches








QS = 2 inches, SR = 2 inches








QS = 2 inches, SR = 8 inches

Answer 1

QS = 6 inches, SR = 10 inches

Answer 2

What they're trying to get you to do is to notice that when you add two sides of a triangle the sum of the lengths of the two sides will be greater than the third length. So, to solve this one, you do the pythagorean thereom using both sides to find the third. Ex. PS = 4 in. So, that is one side of the first triangle. So, let's let that be side A. When you square that, it totals 4^2 = 16. So, side A = 16. Now, we plug the other answers they've given you, and make that = side B and square it. The sum of those will total to side C^2. Then, you just make sure the sum of the two sides is greater than the third. If it does, you have your answer, because the sum of the two sides squared, will be greater than the 3rd side. \[qs=6, sr=10 lets try them\]