Question

)If triangles ABC and DEF are similar and AB = 4 cm, DE= 6 cm, EF = 9 cm and

FD = 12 cm, the perimeter of triangle ABC is:

A) 22 B) 20

C) 21 D) 18 ​

Answer 1

Answer:

Now, we have to find out the perimeter of

∆ ABC

Let ∆ ABC ~ ∆ DEF

$\frac{ab}{de} = \frac{ac}{df} = \frac{bc}{ef} \\ \\ \frac{ab}{de} = \frac{ac}{de} \\ \\ \frac{4}{6} = \frac{ac}{12}$

By cross multiplication we get

$ac \: \: = \frac{4 \times 12}{6} \\ \\ ac = \frac{48}{6} \\ \\ ac = 8cm$

Then consider AB/DE = BC /EF

4/6 = BC /9

BC = (4×9)/6

BC = 36/6

BC = 6cm

Therefore, the perimeter of

∆ ABC = AB + BC + AC

= 4+6+8

= 18 cm

option : D

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