Question

if ∆ABC ~ ∆DEF and EF = 1/3 BC, then ar(∆ABC) : ar(∆DEF) is
(a) 3:1
(b) 1:3
(c) 9:1
(d) 1:9
please explain how?​

Answer 1

Answer:

(A) 3:1 is the correct answer

Step-by-step explanation:

Given,

EF = 1/3 BC

EF/BC = 1/3 ....(1)

Since, Both triangle are similar (Given)

Therefore, All sides will are in ratio

==> AB/DE = BC/EF = AC/DF

But EF /BC = 1/3 (From 1)

BC/ EF = 3/1

So , all Sides BC/ EF = AB/DE = AC/DF = 3/1

Therefore, ∆ ABC : ∆ DEF = 3 : 1

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