# If ∆ABC ~ ∆DEF, AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, find the perimeter of ∆ABC. - Mathematics

Sum

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

#### Solution

AB = 4 cm

DE = 6 cm

EF = 9 cm

FD = 12 cm

Also,

∆ABC ∼ ∆DEF

We have,

∴ (AB)/(ED) = (BC)/(EF) = (AC)/(DF)

⇒ 4/6 = (BC)/9 = (AC)/12

By taking first two terms, we have

⇒ 4/6 = (BC)/9

⇒ BC = ((4 xx 9))/6 = 6 cm

And by taking last two terms, we have,

(BC)/9 = (AC)/12

6/9 = (AC)/12

AC = (6 xx 12)/9 = 8 cm

Now,

Perimeter of ∆ABC = AB + BC + AC

= 4 + 6 + 8

= 18 cm

Thus, the perimeter of the triangle is 18 cm.

Concept: Basic Proportionality Theorem (Thales Theorem)
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 6 Triangles
Exercise 6.3 | Q 7 | Page 68

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