Question

In △ABC, P, Q and R are mid points of sides AB, BC and AC respectively. If AB= 10 cm, BC= 8.4 cm  and AC= 7cm. Find the perimeter of △PQR. ​

Answer 1

Answer:

Answer

Between the triangle ARP and CRQ applying mid point theorem

RP ∥  BC and

RP =21 BC = CQ.

And AR = RC ( R is the mid point of AC )

again PR ∥ BC and AC is the transversal.

Therefore angle ARP = angle RCQ.

Therefore the triangles are congruent by SAS test.

Area ΔARP=AreaΔ RCQ.

By applying the same midpoint theorem we can prove that each of the four triangles have the same area.

So, they divide the triangle into four equal areas.

Now total area = 20 sq. cm.

Therefore area of the Δ PQR is 20 sq.cm divided by 4 = 5 sq.cm

Step-by-step explanation:

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Answer 2

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In △ABC, P, Q and R are mid points of sides AB, BC and AC respectively. If AB= 10 cm, BC= 8.4 cm  and AC= 7cm. Find the perimeter of △PQR. 

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Midpoint Theorem:

The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

AB = 8 cm

⇒ AD = DB = 8 ÷ 2 = 4cm

BC = 7.2 cm

⇒ BE = EC = 7.2 ÷ 2 = 3.6 cm

AC = 6 cm

⇒ AF = FC = 6 ÷ 2 = 3 cm

Apply the Midpoint Theorem:

DF = BE = 3.6 cm

DE = FC = 3 cm

EF = DB = 4 cm

Find the perimeter:

Perimeter = 3.6 + 3 + 4 = 10.6 cm

Answer: 10.6 cm