document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #96383 by solver91311(24713) $\"\"$ $\"About$

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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.\r
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\n" ); document.write( "\n" ); document.write( "If you don't remember Pythagorean triples, then use the Pythagorean theorem,\r
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\n" ); document.write( "\n" ); document.write( " $\"sqrt%2813%5E2-12%5E2%29\"$ = the missing side\r
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\n" ); document.write( "\n" ); document.write( " $\"sqrt%28169-144%29=sqrt%2825%29=5\"$ . Same result, PS = SR = 5, so PR = 10 \n" ); document.write( "

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