Question

in triangle ABC, P, Q are mid pointsof sides AB, BC and AC respectively. If perimeter of triangle ABC is 11 3/4 cm, then perimeter of triangle PQR is ___​

Answer 1

Answer:

Between the triangle ARP and CRQ applying mid point theorem

RP ∥ BC and

RP =

2

1

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