Question

In ∆PQR, A,B,C are the midpoints of PQ,QR,RP respectively. If AB:BC:CA=3:4:5 and QR=20cm, find the perimeter of ∆PQR.

Answer 1

48 cm

Step-by-step explanation:

Given that AB : BC : CA = 3 : 4 : 5

Let, AB = 3x, BC = 4x and CA = 5x.

Now, we know that if we join the middle points of any two sides of a triangle then the length of the line segment formed will be half of the length of the third side of the triangle.

So, PR = 2 × AB = 6x

PQ = 2 × BC = 8x and

QR = 2 × CA = 10x

Now, given that QR = 20 cm = 10x

⇒ x = 2

Therefore, the perimeter of the triangle Δ PQR = PQ + QR + RP

= (8x + 10x + 6x)

= 24x

= 24(2)

= 48 cm. (Answer)