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Q.

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


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a

19cm

b

36cm

c

18cm

d

25cm 

answer is C.

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Detailed Solution

Given,
∆ ABC ~ ∆ DEF,
AB = 4 cm,
DE = 6 cm,
EF = 9 cm and
FD = 12 cm.
The perimeter of a triangle is the sum of all the sides of the triangle and is written as,P=a+b+C , where a and c are the sides and b is the base of a triangle respectively.
By ∆ ABC ~ ∆ DEF,
Thus, AB DE = BC EF = AC DF   which gives us,  AB DE = BC EF 4 6 = BC 9 BC= 36 6 BC=6cm  
In the same way, taking other two sides,
BC EF = AC DF 6 9 = AC 12 AC= 72 9 AC=8cm  
So, perimeter of Δ  ABC is,
P=AB+BC+AC
P=4+6+8
P=18cm.
The perimeter of a triangle ABC is 18cm.
Therefore, the correct option is 3.
 
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