∆ABC is such that AB = 3 cm, BC = 2cm, CA = 2.5 cm. If ∆ABC ~ ∆DEF and EF = 4 cm, then perimeter of ∆DEF is

(a) 7.5 cm   (b) 15 cm   (c) 22.5 cm   (d) 30 cm

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Question 16 ∆ABC is such that AB = 3 cm, BC = 2cm, CA = 2.5 cm. If ∆ABC ~ ∆DEF and EF = 4 cm, then perimeter of ∆DEF is (a) 7.5 cm (b) 15 cm (c) 22.5 cm (d) 30 cm Since ∆ ABC ~ ∆ DEF Sides will be proportional AB/DE=𝐵𝐶/𝐸𝐹=𝐴𝐶/𝐸𝐹 Putting values 3/DE=2/4=2.5/𝐸𝐹 3/DE=1/2=2.5/𝐸𝐹 𝟑/𝑫𝑬=𝟏/𝟐 DE = 2 × 3 DE = 6 cm 𝟏/𝟐=(𝟐.𝟓)/𝑬𝑭 EF = 2 × 2.5 EF = 5 cm Now, Perimeter of Δ DEF = DE + EF + DF = 6 + 5 + 4 = 15 cm So, the correct answer is (b)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.