document.write( "Question 1143018: In a triangle PQR, If QE and RF are two medians and they intersect each other at angle of 900 than find the length of side QR if length of PQ = 5 cm. and PR = 6cm. \n" ); document.write( "

Algebra.Com's Answer #763860 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Let H be the point of intersection of the two medians.

\n" ); document.write( "The medians of a triangle meet in such a way that each median is divided into two parts with lengths in the ratio 1:2.

\n" ); document.write( "Let FH be x; then HR is 2x. Let EH be y; then HQ is 2y.

\n" ); document.write( "In right triangle EHR, $\"%28y%29%5E2%2B%282x%29%5E2+=+3%5E2\"$ (1)

\n" ); document.write( "In right triangle FHQ, $\"%28x%29%5E2%2B%282y%29%5E2+=+2.5%5E2\"$ (2)

\n" ); document.write( "In right triangle EHF, $\"x%5E2%2By%5E2+=+%28EF%29%5E2\"$

\n" ); document.write( "And by similar triangles, QR is twice EF.

\n" ); document.write( "Combine equations (1) and (2) in an appropriate way to find the value of x^2+y^2 and use that to find the length of QR. \n" ); document.write( "

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