Question 1143018
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Let H be the point of intersection of the two medians.<br>
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.<br>
Let FH be x; then HR is 2x.  Let EH be y; then HQ is 2y.<br>
In right triangle EHR, {{{(y)^2+(2x)^2 = 3^2}}} (1)<br>
In right triangle FHQ, {{{(x)^2+(2y)^2 = 2.5^2}}} (2)<br>
In right triangle EHF, {{{x^2+y^2 = (EF)^2}}}<br>
And by similar triangles, QR is twice EF.<br>
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.