Q) If Δ ABC ~ Δ DEF and AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, find the perimeter of Δ ABC.

Ans: Let’s start with the diagram for he given question:

Step 1: Since we are given that Δ ABC ~ Δ DEF,

∴

Step 2: Taking first two terms, we have:

∴ BC =

By substituting the given values, we get:

BC =

= = 6 cm

Step 3: Similarly, from last two terms, we get:

∴

∴ AC =

By substituting the given values, we get:

AC =

= = 8 cm

Step 4: Now, we have AB = 4 cm, BC = 6 cm, AC = 8 cm

Hence, perimeter of Δ ABC

= AB + BC + AC

= 4 + 6 + 8 = 18 cm

Therefore, perimeter of Δ ABC is 18 cm.

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