SOLUTION: 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.

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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.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let H be the point of intersection of the two medians.

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.

Let FH be x; then HR is 2x. Let EH be y; then HQ is 2y.

In right triangle EHR, %28y%29%5E2%2B%282x%29%5E2+=+3%5E2 (1)

In right triangle FHQ, %28x%29%5E2%2B%282y%29%5E2+=+2.5%5E2 (2)

In right triangle EHF, x%5E2%2By%5E2+=+%28EF%29%5E2

And by similar triangles, QR is twice EF.

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.