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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