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
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)
Made by
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 and Computer Science at Teachoo
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