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If DE ∥ BC, AD = 1.5 cm… (Class 10 Maths Basic 2026, Q8)

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MathsCBSE Class 10 · Basic · Board exam 2026, set 430/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2026: question 8

Set in the CBSE Class 10 board exam of 2026, 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 , cm, cm and 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 D on side AB and E on side AC, DE parallel to BC. Marked: AD = 1.5 cm, DB = 3 cm (along side AB), EC = 2 cm (along side AC). See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/2/1.

Hints

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

Hint 1

Which theorem relates the segments cut on two sides of a triangle by a line parallel to the third side?

Hint 2

Use AD/DB = AE/EC to find AE first.

Hint 3

AE = 2 × (1.5/3) = 1 cm; now add EC to get AC.

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. Since , by the Basic Proportionality Theorem: , so cm.

    ½ mark

  2. cm. Hence option (B).

    ½ mark

Answer: AC = 3 cm, option (B)

Where the marks are

  • Applies BPT to get AE = 1 cm and AC = AE + EC = 3 cm, choosing 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 paper2026 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.