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In △ ABC, DE ∥ BC (as shown in… (Class 10 Maths 2024, Q12)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/3/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 12

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, section A, question 12, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q12 · 1 mark · MCQTriangles

In ABC, DE BC (as shown in the figure). If AD = 2 cm, BD = 3 cm, BC = 7.5 cm, then the length of DE (in cm) is:

  1. (A)2.5
  2. (B)3
  3. (C)5
  4. (D)6

Figure in the paper: Triangle ABC with vertex A at the top, B at bottom left and C at bottom right. D lies on AB and E lies on AC, with DE drawn parallel to BC. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

DE ∥ BC makes triangle ADE similar to triangle ABC.

Hint 2

Remember to use AB = AD + DB, not DB alone.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. cm. Since DE ∥ BC, (AA).

  2. , so cm. This is option (B).

    1 mark

Answer: 3 cm, option (B)

Where the marks are

  • Uses similarity to get DE = 3 cm, option (B) (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Triangles, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 30/3/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.