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

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(A) According to Apollonius's Theorem for $\Delta PQR$ with median $\overline{PS}$:$PQ^2 + PR^2 = 2(PS^2 + QS^2)$Given $PQ = 9$,$PR = 40$,and $PS = 20

Vedclass · Accepted Answer

$41$

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(A) According to Apollonius's Theorem for $\Delta PQR$ with median $\overline{PS}$:$PQ^2 + PR^2 = 2(PS^2 + QS^2)$Given $PQ = 9$,$PR = 40$,and $PS = 20.5$:$9^2 + 40^2 = 2(20.5^2 + QS^2)$$81 + 1600 = 2(420.25 + QS^2)$$1681 = 2(420.25 + QS^2)$$840.5 = 420.25 + QS^2$$QS^2 = 840.5 - 420.25 = 420.25$$QS = \sqrt{420.25} = 20.5$Since $\overline{PS}$ is a median,$S$ is the midpoint of $\overline{QR}$,so $QR = 2 	imes QS = 2 	imes 20.5 = 41$.

In $\Delta PQR$,$\overline{PS}$ is a median. If $PQ = 9$,$PR = 40$ and $PS = 20.5$,find $QR$.

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