Question 17 In the figure, if DE∥ BC, AD = 3cm, BD = 4 cm and BC = 14 cm, then DE equals (a) 7 cm (b) 6 cm (c) 4 cm (d) 3 cm
Since DE ∥ BC
∠ ADB = ∠ ABD
∠ AED = ∠ ACB
Thus, by AA Similarity
Δ ADE ~ Δ ABC
Since sides are proportional in similar triangles
𝐴𝐷/𝐴𝐵=𝐷𝐸/𝐵𝐶
𝟑/(𝟑 + 𝟒)=𝑫𝑬/𝟏𝟒
3/7=𝐷𝐸/14
3/7 × 14 = DE
3 × 2 = DE
6 = DE
DE = 6 cm
So, the correct answer is (B)
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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