In Delta PQR,A,B,and C are the mid-points of | vedclass

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Question

(C) According to the Mid-point Theorem,the line segment joining the mid-points of two sides of a triangle is parallel to the third side and half of it

Vedclass · Accepted Answer

$37.2$

Vedclass · Answer

(C) According to the Mid-point Theorem,the line segment joining the mid-points of two sides of a triangle is parallel to the third side and half of its length.In $\Delta PQR$,since $A$ and $C$ are mid-points of $PQ$ and $RP$ respectively,$AC = \frac{1}{2} QR$.Similarly,$AB = \frac{1}{2} RP$ and $BC = \frac{1}{2} PQ$.The perimeter of $\Delta ABC = AB + BC + AC = \frac{1}{2} RP + \frac{1}{2} PQ + \frac{1}{2} QR = \frac{1}{2} (PQ + QR + RP)$.Given that the perimeter of $\Delta ABC = 18.6 \, cm$.Therefore,$18.6 = \frac{1}{2} 	imes (	ext{Perimeter of } \Delta PQR)$.Perimeter of $\Delta PQR = 18.6 	imes 2 = 37.2 \, cm$.

In $\Delta PQR$,$A$,$B$,and $C$ are the mid-points of $PQ$,$QR$,and $RP$ respectively. If the perimeter of $\Delta ABC$ is $18.6 \, cm$,then the perimeter of $\Delta PQR$ is $\ldots \ldots \ldots cm$.

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