Question 2 - NCERT Exemplar - MCQ - Chapter 6 Class 10 Triangles

Last updated at April 16, 2024 by

D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE ∥ BC. Then, length of DE (in cm) is

(A) 2.5  

(B) 3  

(C) 5  

(D) 6

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Transcript

Question 2 D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE ∥ BC. Then, length of DE (in cm) is (A) 2.5 (B) 3 (C) 5 (D) 6 Since DE ∥ BC ∠ ADB = ∠ ABD ∠ AED = ∠ ACB Thus, by AA Similarity Δ ADE ~ Δ ABC (Corresponding angles) (Corresponding angles) Since sides are proportional in similar triangles 𝐴𝐷/𝐴𝐵=𝐷𝐸/𝐵𝐶 𝟐/(𝟐 + 𝟑)=𝑫𝑬/(𝟕.𝟓) 2/5=𝐷𝐸/7.5 2/5 × 7.5 = DE 2 × 1.5 = DE 3 = DE DE = 3 cm 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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.