If ∆ ABC ∼ ∆ XYZ, AB = 6 cm, XY = 8 cm, YZ = 12 cm and ZX = 16 cm, then find the perimeter of ∆ ABC.

Question

Question

This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 06 Jun, 2025 Shift 3)

Answer 1

Given:

∆ABC ~ ∆XYZ

AB = 6 cm, XY = 8 cm

YZ = 12 cm, ZX = 16 cm

Formula used:

If two triangles are similar, their corresponding sides are proportional:

\(AB/XY = BC/YZ = AC/ZX\)

Perimeter of ∆ABC = AB + BC + AC

Calculation:

Task Id 1582 (2)

AB/XY = BC/YZ = AC/ZX

⇒ 6/8 = BC/12 = AC/16

First, find BC:

⇒ 6/8 = BC/12

⇒ BC = (6 × 12)/8 = 9 cm

AC:

⇒ 6/8 = AC/16

⇒ AC = (6 × 16)/8 = 12 cm

Now, calculate the perimeter of ∆ABC:

⇒ Perimeter = AB + BC + AC

⇒ Perimeter = 6 + 9 + 12

⇒ Perimeter = 27 cm

∴ The correct answer is option (3).

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