Question 697524: PQRS is a rectangle in which PQ=10cm and Ps=6cm.T is a point on PQ such that RST is an isosceles triangle whose equal side are RS and ST.Find RT.
The main Problem I face here is Placing the P,Q,R and S.I always get them wrong,how should the placing be done.
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! I just draw a rectangle and start at any corner and label them clockwise starting with the first letter, P, then Q, R, S. Put a point on PQ and label it T. The isosceles triangle STR, has ST = SR = 10. Then solve two right triangle problems, one for PT, the second for RT as follows.
(1) PT^2 = 10^2 - 6^@ or
(2) PT = sqrt(64) or
(3) PT = 8 from which you get
(4) TQ = 10 - 8 or
(5) TQ = 2
Now use right triangle TQR to find
(6) RT^2 = TQ^2 + QR^@ or
(7) RT^2 = 2^2 + 6^2 or
(8) RT^2 = 40 or
(9) RT = 2 cm
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