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It is given that ∆ ABC ~ ∆ DFE, ∠ A = 30°, ∠ C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then, the following is true:

(A) DE = 12 cm, ∠ F = 50°  

(B) DE = 12 cm, ∠ F = 100°

(C) EF = 12 cm, ∠ D = 100°  

(D) EF = 12 cm, ∠ D = 30°

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Question 11 It is given that ∆ ABC ~ ∆ DFE, ∠ A = 30°, ∠ C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then, the following is true: (A) DE = 12 cm, ∠ F = 50° (B) DE = 12 cm, ∠ F = 100° (C) EF = 12 cm, ∠ D = 100° (D) EF = 12 cm, ∠ D = 30° So, our triangles look like Now, ∠ D = ∠ A = 30° ∠ E = ∠ C = 50° And, in Δ DEF By Angle sum property ∠ D + ∠ F + ∠ E = 180° 30° + ∠ F + 50° = 180° 80° + ∠ F = 180° ∠ F = 180 − 80° ∠ F = 100° Since ∠ F = 100° & ∠ D = 30° So, only option (B) and option (D) can be the answer Since ∆ ABC ~ ∆ DFE Corresponding sides are proportional ∴ 𝐴𝐵/𝐷𝐹=𝐴𝐶/𝐷𝐸=𝐵𝐶/𝐸𝐹 Putting values 𝟓/(𝟕.𝟓)=𝟖/𝑫𝑬=𝑩𝑪/𝑬𝑭 Comparing 𝟓/(𝟕.𝟓)=𝟖/𝑫𝑬 2/3=8/𝐷𝐸 DE = 8 × 3/2 DE = 12 cm Thus, DE = 12 cm & ∠ F = 100° So, the correct answer is (B)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.