If Δ ABC ~ Δ DEF and AB = 4 cm, DE = 6 cm, EF = 9 cm

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,

∴ $\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{FD}$

Step 2: Taking first two terms, we have:

$\frac{AB}{DE} = \frac{BC}{EF}$

∴ BC = $\frac{AB \times EF}{DE}$

By substituting the given values, we get:

BC = $\frac{4 \times 9}{6}$

= $\frac{36}{6}$ = 6 cm

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

∴ $\frac{AB}{DE} = \frac{AC}{FD}$

∴ AC = $\frac{AB \times FD}{DE}$

By substituting the given values, we get:

AC = $\frac{4 \times 12}{6}$

= $\frac{48}{6}$ = 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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