In Delta PQR, overline{PS} is a median. If PQ | vedclass

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(A) Given that $\overline{PS}$ is a median of $\Delta PQR,$ it divides the side $QR$ into two equal parts. Thus,$QS = SR = 18.5.$Since $PS = QS = SR =

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$35$

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(A) Given that $\overline{PS}$ is a median of $\Delta PQR,$ it divides the side $QR$ into two equal parts. Thus,$QS = SR = 18.5.$Since $PS = QS = SR = 18.5,$ the point $S$ is the circumcenter of $\Delta PQR$ with respect to the side $QR,$ implying $\angle QPR = 90^\circ$ (by the property that if the median to a side is half the length of that side,the triangle is a right-angled triangle).In the right-angled $\Delta PQR,$ by the Pythagorean theorem:$PQ^2 + PR^2 = QR^2$$QR = QS + SR = 18.5 + 18.5 = 37$$12^2 + PR^2 = 37^2$$144 + PR^2 = 1369$$PR^2 = 1369 - 144 = 1225$$PR = \sqrt{1225} = 35.$

In $\Delta PQR,$ $\overline{PS}$ is a median. If $PQ = 12$ and $PS = QS = 18.5,$ find $PR$.

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