Question

In triangle abc, p and q are the midpoints of ab and ac respectively.bc + pq = 21 cm then find bc.​

Answer 1

Given :-

In a triangle ABC, P and Q are the mid points of AB and AC.

BC + PQ = 21 cm

To find :-

The length of BC .

Solution:-

Given that

In a ∆ ABC,

The Mid point of AB = P

The Mid point of AC = Q

We know that

Midpoint Theorem :

"The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side”.

Therefore, PQ || BC and

PQ = BC/2 -----------(1)

Given that

BC + PQ = 21 cm

=> BC + (BC/2) = 21

=> (2BC+BC)/2 = 21

=> 3BC /2 = 21

=> 3BC = 21×2

=> 3BC = 42

=> BC = 42/3

=> BC = 14 cm

Answer :-

The length of the side BC is 14 cm

Used Theorem :-

Midpoint Theorem :

Midpoint Theorem :"The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side”.