Question

the figure p and q are the midpoints of the sides ab and ac respectively of triangle ABC. if PQ equals to 3.5 cm and AB equals to AC equals to 9 CM then the perimeter of triangle ABC is

Answer 1

The perimeter of triangle is 25 cm

If PQ is 3.5 cm then BC will be 2PQ (mid point theorem)

So BC = 3.5 x 2 = 7cm

Perimeter = AB + BC + AC

= 9 + 9 + 7

= 25 cm

Answer 2

Given,

P and Q are the midpoints of the sides AB and AC respectively of triangle ABC.

PQ = 3.5 cm

AB = AC = 9 cm

To find,

The perimeter of ∆ ABC.

Solution,

The perimeter of ∆ ABC will be 25 cm.

We can easily solve this problem by following thw given steps.

According to the question,

P and Q are the midpoints of the sides AB and AC respectively of triangle ABC.

So, according to the mid-point theorem,

The length of the parallel side (BC) in the triangle will be twice the line joining the two midpoints on the other two sides of the triangle (PQ).

PQ = 3.5 cm

BC = 2×3.5

BC = 2×3.5BC = 7 cm

AB = AC = 9 cm

We know that the perimeter of a triangle is the sum of all three sides.

The perimeter of ∆ ABC (P) = AB+AC+BC

P = (9+9+7) cm

P = 25 cm

Hence, the perimeter of ∆ ABC is 25 cm.