In Delta ABC,P and Q are the midpoints of AB | vedclass

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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 is half the

Vedclass · Accepted Answer

$14$

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 is half the length of the third side.In $\Delta ABC$,since $P$ and $Q$ are midpoints of $AB$ and $AC$ respectively,we have $PQ = \frac{1}{2} BC$.Given that $BC + PQ = 21 	ext{ cm}$.Substituting $PQ = \frac{1}{2} BC$ into the equation,we get $BC + \frac{1}{2} BC = 21$.This simplifies to $\frac{3}{2} BC = 21$.Multiplying both sides by $\frac{2}{3}$,we get $BC = 21 	imes \frac{2}{3} = 14 	ext{ cm}$.

In $\Delta ABC$,$P$ and $Q$ are the midpoints of $AB$ and $AC$ respectively. If $BC + PQ = 21 \text{ cm}$,then find the length of $BC$.

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