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△ ABC is shown. DE is parallel… (Class 10 Maths 2024, Q6)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 6

Set in the CBSE Class 10 board exam of 2024, paper 30/2/1, section A, question 6, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q6 · 1 mark · MCQTriangles

In the given figure is shown. is parallel to . If cm, cm and cm, then is equal to

  1. (A) cm
  2. (B) cm
  3. (C) cm
  4. (D) cm

Figure in the paper: Triangle ABC with vertex A at the top, B bottom-left, C bottom-right. D lies on side AB and E lies on side AC, with segment DE drawn parallel to base BC. Labels: AD = 5 cm (along AD), DB = 2.5 cm (along DB), BC = 12 cm along the base. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/2/1.

Hints

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

Hint 1

The small and big triangles are similar.

Hint 2

AB = AD + DB = 7.5 cm.

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. ⇒ (AA), so .

  2. cm. Option (C).

    1 mark

Answer: 8 cm, option (C)

Where the marks are

  • Uses similarity ratio AD/AB to get DE = 8 cm (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 30/2/1 (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.