In Delta PQR,PM is a median and N is the midp | vedclass

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Question

(A) $1$. In $\Delta PQR$,$PM$ is a median,so it divides the triangle into two triangles of equal area: $	ext{ar}(PQM) = 	ext{ar}(PRM) = \frac{1}{2}

Vedclass · Accepted Answer

$144$

Vedclass · Answer

(A) $1$. In $\Delta PQR$,$PM$ is a median,so it divides the triangle into two triangles of equal area: $	ext{ar}(PQM) = 	ext{ar}(PRM) = \frac{1}{2} 	ext{ar}(PQR)$.$2$. In $\Delta PQM$,$QN$ is a median because $N$ is the midpoint of $PM$. Therefore,$	ext{ar}(PQN) = 	ext{ar}(QNM) = \frac{1}{2} 	ext{ar}(PQM)$.$3$. Given $	ext{ar}(PQN) = 36 	ext{ cm}^2$,we have $	ext{ar}(PQM) = 2 	imes 	ext{ar}(PQN) = 2 	imes 36 = 72 	ext{ cm}^2$.$4$. Since $	ext{ar}(PQM) = \frac{1}{2} 	ext{ar}(PQR)$,it follows that $	ext{ar}(PQR) = 2 	imes 	ext{ar}(PQM) = 2 	imes 72 = 144 	ext{ cm}^2$.

In $\Delta PQR$,$PM$ is a median and $N$ is the midpoint of $PM$. If $\text{ar}(PQN) = 36 \text{ cm}^2$,then $\text{ar}(PQR) = \dots \text{ cm}^2$.

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