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(B) According to the Midpoint Theorem,the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half of its

Vedclass · Accepted Answer

$11.5$

Vedclass · Answer

(B) According to the Midpoint Theorem,the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half of its length.Let the sides of $\Delta ABC$ be $AB$,$BC$,and $AC$.Since $P$,$Q$,and $R$ are midpoints of sides $AB$,$BC$,and $AC$ respectively,the sides of $\Delta PQR$ are $PQ = \frac{1}{2} AC$,$QR = \frac{1}{2} AB$,and $PR = \frac{1}{2} BC$.The perimeter of $\Delta PQR = PQ + QR + PR = \frac{1}{2} AC + \frac{1}{2} AB + \frac{1}{2} BC = \frac{1}{2} (AB + BC + AC)$.Given that the perimeter of $\Delta ABC = AB + BC + AC = 23 \, cm$.Therefore,the perimeter of $\Delta PQR = \frac{1}{2} 	imes 23 = 11.5 \, cm$.

In $\Delta ABC$,$P$,$Q$,and $R$ are the midpoints of the sides. If the perimeter of $\Delta ABC$ is $23 \, cm$,then find the perimeter of $\Delta PQR$ in $cm$.

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