Question

If triangle ABC ~ PQR, perimeter of triangle ABC =20 cm perimeter of triangle PQR=40 cm and PR=8cm find the length of AC

Answer 1

Step-by-step explanation:

We have ,

∆ABC ~ ∆PQR

→AB/PQ = BC/QR = AC/PR .

→AB/PQ = BC/QR = AC/PR = k. (say)

→AB = PQk

AC=PRk

BC =QRk

→(AB+BC + CA )/(PQ + QR +RQ)= k

→AC/PR = perimeter of ∆ABC/perimeter of ∆PQR

→AC/8cm =20/40

→AC=4cm

Answer 2

Given:

Triangle ABC~PQR

The perimeter of triangle ABC= 20cm

The perimeter of triangle PQR= 40cm

PR= 8cm

To find:

Length of AC

Solution:

Let's follow the steps given below to find out the answer-

We are given that the triangle ABC is similar to triangle PQR.

So, we know that the ratio of the corresponding sides of similar triangles is equal to the ratio of its perimeters.

AB/PQ= BC/QR= AC/PR= Perimeter of the triangle ABC/ Perimeter of the triangle PQR

Since we are given that PR= 8 cm, we will equate AC/ PR to the ratio of perimeters.

AC/ 8= 20/40

AC=8/2

AC= 4cm

Therefore, the length of AC is 4cm.