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If DE ∥ BC, AD = 1.5 cm… (Class 10 Maths Basic 2025, Q8)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2025: question 8

Set in the CBSE Class 10 board exam of 2025, paper 430/2/1, section A, question 8, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q8 · 1 mark · MCQTriangles

In the given figure, if DE BC, AD = 1.5 cm, DB = 3 cm and EC = 2 cm, the length of AC is :

  1. (A)1.5 cm
  2. (B)3 cm
  3. (C)3.5 cm
  4. (D)4.5 cm

Figure in the paper: Triangle ABC with A at the top. D lies on side AB and E lies on side AC, with DE parallel to BC. AD = 1.5 cm and DB = 3 cm are marked on AB; EC = 2 cm is marked on AC. Arrows show DE parallel to BC. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/2/1.

Hints

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

Hint 1

DE ∥ BC — which theorem applies?

Hint 2

Find AE first, then add EC.

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. By the Basic Proportionality Theorem, , so , giving AE = 1 cm.

  2. AC = AE + EC = 1 + 2 = 3 cm, which is option (B).

    1 mark

Answer: 3 cm, option (B)

Where the marks are

  • Uses BPT to get AE = 1 cm and AC = 3 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 paper2025 board paper, set 430/2/1 (Basic): 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.