Question

the length of the line joining the midpoint of the triangle is 5.5 cm what will the length of side parallel to it the length of the​

Answer 1

Answer :-

• The length of side parallel to PQ i.e. BC = 11 cm

Given :-

• P is mid-point of AB
• Q is mid-point of AC
• PQ = 5.5 cm

To Find :-

• BC = ?

Explanation :-

In order to find the length of BC, we need to understand a theorem.

• Mid-Point Theorem - The mid-point theorem states that "The line segment joining the mid-points of two sides of triangle is Parallel and Half of third side".

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂

$\boxed { \boxed { \bf \odot In \: \triangle \: ABC }}$

$\rm \implies \text {P is the mid point of AB} \qquad \bold{[Given]}$

$\rm \implies \text {Q is the mid point of AC} \qquad \bold{[Given]}$

$\rm \therefore PQ \parallel BC \qquad \bold{[By \: Mid \: Point \: theorem]}$

$\rm \therefore PQ = \dfrac{1}{2} \: BC \qquad \bold{[By \: Mid \: Point \: theorem]}$

Now,

$\rm \implies BC = 2(PQ)$

$\rm \implies BC = 2 \times PQ$

$\rm \implies BC = 2 \times 5.5$

$\underline { \boxed { \bf \implies BC = 11 cm }}$

Hence, the length of side parallel to PQ i.e. BC is 11 cm.

@Agamsain