Question

7. In A ABC, P, Q and R are the midpoints of
AB, BC and AC respectively. If AB = 8 cm,
BC = 9 cm and AC = 10.6 cm, find the perimeter
of APQR.​

Answer 1

Given Question :-

• In A ABC, P, Q and R are the midpoints of AB, BC and CA respectively. If AB = 8 cm, BC = 9 cm and CA = 10.6 cm, then find the perimeter of quadrilateral APQR.

Answer :-

Given :-

• P is the midpoint of AB.

• Q is the midpoint of BC.

• R is the midpoint of CA.

• AB = 8 cm

• BC = 9 cm

• CA = 10.6 cm

To Find :-

• Perimeter of quadrilateral APQR.

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.

⇛ Q is the midpoint of BC.

This implies, PQ || AC and PQ = 1/2 AC

It means , PQ || AR and PQ = AR

This implies, APQR is a parallelogram.

As, P is midpoint of AB.

⇛ AP = 4 cm

Also, R is midpoint of AC.

⇛ AR = 5.3 cm

$\tt \:  \longrightarrow \: Now, \: perimeter \: of \: quadrilateral \: APQR \\ \: \: \: \: \: \tt \:  \longrightarrow \: \: = 2 \times (AP + AR) \\ \: \: \: \: \: \: \tt \:  \longrightarrow \: \: = 2 \times (4 \: + \: 5.3) \\ \: \: \: \: \tt \:  \longrightarrow \: = 2 \times 9.3 \\ \: \: \: \: \tt \:  \longrightarrow \: \: = \: 18.6 \: cm \:$