Question

If ∆ABC ~ ∆PQR, then the perimeter of the triangle PQR (in cm) is ______.

पर्याय

• 12

• 24

• 18

• 20

Answer 1

If ∆ABC ~ ∆PQR, then the perimeter of the triangle PQR (in cm) is 24.

Explanation:

Given, ∆ABC ~ ∆PQR

So, corresponding sides are proportional.

For ΔABC:

AB = 3 cm, BC = 4 cm, AC = 5 cm

For ΔPQR:

PR = 10 cm   ....(corresponds to AC)

Scale factor = `PR/AC`

= `10/5`

= 2

Multiply all sides of ΔABC by 2:

PQ = AB × 2

= 3 × 2

= 6 cm

QR = BC × 2

= 4 × 2

= 8 cm

PR = AC × 2

= 5 × 2

= 10 cm

Perimeter of the ΔPQR:

PQ + QR + PR

= 6 + 8 + 10

= 24 cm