Question

8. In ∆ABC, P, Q and R are the midpoints of
AB, BC and CA respectively. If AB = 8.2 cm,
BC = 6.4 cm and CA = 7.5 cm, then find the
perimeter of quadrilateral PBOR.​

Answer 1

Answer:

Given Question :-

In A ABC, P, Q and R are the midpoints of AB, BC and CA respectively. If AB = 8.2 cm, BC = 6.4 cm and CA = 7.5 cm, then find the perimeter of quadrilateral PBQR.

Answer :-

Given :-

P is the midpoint of AB.

Q is the midpoint of BC.

R is the midpoint of CA.

AB = 8.2 cm

BC = 6.4 cm

CA = 7.5 cm

To Find :-

Perimeter of quadrilateral PBQR.

Method used :-

The midpoint theorem states that “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.”

Solution:-

In triangle ABC.

⇛ P is the midpoint of AB.

⇛ R is the midpoint of AC.

This implies, PR || BC and PR = 1/2 BC

It means , PR || BQ and PR = BQ

This implies, PBQR is a parallelogram.

As, Q is midpoint of BC.

⇛ BQ = 3.2 cm

Also, P is midpoint of AB.

⇛ BP = 3.2 cm

Step-by-step explanation: