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(B) Given that $P$, $Q$, and $R$ are the midpoints of $AB$, $BC$, and $CA$ respectively.By the Midpoint Theorem, the line segment joining the midpoint

Vedclass · Accepted Answer

$14.6$

Vedclass · Answer

(B) Given that $P$, $Q$, and $R$ are the midpoints of $AB$, $BC$, and $CA$ respectively.By 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.In $\Delta ABC$, $R$ is the midpoint of $AC$ and $Q$ is the midpoint of $BC$. Thus, $RQ = \frac{1}{2} AB = \frac{8.2}{2} = 4.1 	ext{ cm}$.Also, $P$ is the midpoint of $AB$ and $Q$ is the midpoint of $BC$. Thus, $PQ = \frac{1}{2} AC = \frac{7.5}{2} = 3.75 	ext{ cm}$.Since $P$ is the midpoint of $AB$, $PB = \frac{1}{2} AB = \frac{8.2}{2} = 4.1 	ext{ cm}$.Since $Q$ is the midpoint of $BC$, $BQ = \frac{1}{2} BC = \frac{6.4}{2} = 3.2 	ext{ cm}$.The quadrilateral $PBQR$ has sides $PB$, $BQ$, $QR$, and $RP$.Perimeter $= PB + BQ + QR + RP$.We know $RP = \frac{1}{2} BC = 3.2 	ext{ cm}$.Perimeter $= 4.1 + 3.2 + 4.1 + 3.2 = 14.6 	ext{ cm}$.

In $\Delta ABC$, $P$, $Q$, and $R$ are the midpoints of $AB$, $BC$, and $CA$ respectively. If $AB = 8.2 \text{ cm}$, $BC = 6.4 \text{ cm}$, and $CA = 7.5 \text{ cm}$, then find the perimeter of quadrilateral $PBQR$. (in $\text{ cm}$)

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