SOLUTION: PQR is an isosceles trianlge such that QP=QR=13 cm and the altitude PS=12 cm. Find the length PR.

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Question 205229: PQR is an isosceles trianlge such that QP=QR=13 cm and the altitude PS=12 cm. Find the length PR.
Answer by solver91311(24713) About Me  (Show Source):
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If PS is an altitude, then you know two things. 1. S lies on the segment QR and 2. PS forms a right angle with QR.

Therefore PQS is a right triangle with a hypotenuse (PQ) of 13 and a long leg (PS) of 12. Either recognizing two numbers from the Pythagorean Triple 13-12-5, or using the Pythagorean Theorem, you can calculate the measure of QS, which is 5.

Knowing that QS = 5, we can determine that SR = QR - QS = 13 - 5 = 8.

Now consider the right triangle PSR with legs PS = 12 and SR = 8.

, so:






John