Question

ABC is an eqilateral TRIANGLE. IF P AND Q ARE TTHE MID POINTS OF AB AND AC RESPECTIVELY AND PQ IS 3CM THEN THE VALUE OF PA AND AQ IS

Answer 1

P and Q are the mid point of AB and AC respectively
On joining P and Q, PQ line will be parallel to line BC
By mid point theorm
1/2 of BC =PQ
BC= 2 PQ
BC=6 cm
As ABC is an equilatral Δ then AB=BC=CA
therefor P is mid point of AB ,Similarly Q is mid point of AC
PA=AQ=6/2=3cm 

Answer 2

• The value of PA is equal to 3 cm .
• The value of AQ is also equal to 3 cm .

Given :-

• ABC is an eqilateral triangle .
• P and Q are the mid points of side AB and AC respectively .
• PQ = 3 cm .

Concept used :-

• Length of all sides of an eqilateral triangle are equal in measure .
• Mid point theorem :- The line segment joining the midpoint of two sides of a triangle is parallel and half of the length of the third side .

Solution :-

from given data we have,

→ AP = PB { since P is mid point of AB }

→ AQ = QC { since Q is mid point of AC }

Now, BC is third side of the ∆ABC .

So,

→ PQ = (1/2)•BC { By mid point theorem }

→ BC = 2•PQ

putting given value of PQ as 3 cm,

→ BC = 2 × 3

→ BC = 6 cm .

then,

→ AB = AC = BC = 6 cm { All sides of an eqilateral triangle are equal in measure }

therefore,

→ PA = (1/2)•AB { since P is mid point of AB }

→ PA = (1/2) × 6

→ PA = 3 cm (Ans.)

and,

→ AQ = (1/2)•AC { since Q is mid point of AC }

→ AQ = (1/2) × 6

→ AQ = 3 cm (Ans.)

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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