SOLUTION: PQR is an isosceles triangle such that , QP=QR=13cm and the altitude PS=12cm . Find the length of PR ? PLS HELP . Thanks

Algebra ->  Pythagorean-theorem -> SOLUTION: PQR is an isosceles triangle such that , QP=QR=13cm and the altitude PS=12cm . Find the length of PR ? PLS HELP . Thanks       Log On


   

Question 131726: PQR is an isosceles triangle such that , QP=QR=13cm and the altitude PS=12cm . Find the length of PR ? PLS HELP . Thanks
Answer by solver91311(24713) About Me  (Show Source):
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In an isosceles triangle, the altitude on the base is a perpendicular bisector of the base, so we know that PS = SR and that PR = PS + SR. Now, if you remember Pythagorean triples which are sets of three integers that form a right triangle, you will recall that a triangle with sides of 5, 12, and 13 form a right triangle. That means either PS or SR have to be length 5 and therefore the base, PR, must be length 10.

If you don't remember Pythagorean triples, then use the Pythagorean theorem,

sqrt%2813%5E2-12%5E2%29 = the missing side

sqrt%28169-144%29=sqrt%2825%29=5. Same result, PS = SR = 5, so PR = 10