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Home » If ∆ABC ∼ ∆DEF, AB = 4 cm, DE = 6, EF = 9 cm and FD = 12 cm, then find the perimeter of ∆ABC.
If ∆ABC ∼ ∆DEF, AB = 4 cm, DE = 6, EF = 9 cm and FD = 12 cm, then find the perimeter of ∆ABC.
CBSE | Class 10 | Exercise 6.3 | Maths | NCERT Exemplar | Triangles
If ∆ABC ∼ ∆DEF, AB = 4 cm, DE = 6, EF = 9 cm and FD = 12 cm, then find the perimeter of ∆ABC.

Solution:

According to the given question,

AB\text{ }=\text{ }4\text{ }cm,

DE\text{ }=\text{ }6\text{ }cm

EF\text{ }=\text{ }9\text{ }cm

FD\text{ }=\text{ }12\text{ }cm

Also,

∆ABC ∼ ∆DEF

We have,

\therefore \frac{AB}{ED}=\frac{BC}{EF}=\frac{AC}{DF}

\Rightarrow \frac{4}{6}=\frac{BC}{9}=\frac{AC}{12}

On taking first two terms, we obtain

\Rightarrow \frac{4}{6}=\frac{BC}{9}

\Rightarrow BC=\frac{\left( 4\times 9 \right)}{6}=6cm

And now on taking last two terms, we obtain,

\frac{BC}{9}=\frac{AC}{12}

\frac{6}{9}=\frac{AC}{12}

AC=\frac{6\times 12}{9}=8cm

Now,

Perimeter\text{ }of\text{ }\Delta ABC\text{ }=\text{ }AB\text{ }+\text{ }BC\text{ }+\text{ }AC

=\text{ }4\text{ }+\text{ }6\text{ }+\text{ }8\text{ }=\text{ }18\text{ }cm

As a result, 18 cm is the perimeter of the triangle.

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