Question

In equilateral triangle ABC, P and Q are the mid-points of sides AB and BC respectively . If the perimeter of triangle ABC is 9 cm, then find the perimeter of quadrilateral PBCQ.​

Answer 1

Answer:

The perimeter of Quadrilateral PBCQ is $7.5cm$

Step-by-step explanation:

All three sides of Equilateral Triangle are of same length.

Let $x$ be the length of each side,

Thus,      Perimeter = $x+x+x=3x$

It is given that Perimeter is 9 cm,

Thus,     $3x=9$

⇒  $x=\frac{9}{3}=3 cm$

That is, the length of each side of given Equilateral Triangle will be 3 cm.

Now, the midpoints of two sides are joined. Then a Trapezium will be formed as shown in figure.

Here we are supposed to calculate the perimeter of this Trapezium.

Cleary the Base of the Trapezium is same as that of original Equilateral triangle, hence its length will be $3 cm$.

Also, the two non-parallel sides are of same length which is half of the length of side of original Equilateral triangle, that is half of 3 = 1.5 cm each.

Now we need to calculate the length of remaining side to get the perimeter. For that we can use Basic Proportionality Theorem.

let $x$ be the length of that side.

⇒ $\frac{x}{3} =\frac{1.5}{3}$

⇒ $x=1.5$

Therefore, Perimeter of Quadrilateral PBCQ is $1.5+1.5+1.5+3=7.5cm$