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In Δ ABC, DE ∥ AB. If AB… (Class 10 Maths SQP 2023-24, Q8)

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MathsCBSE Class 10 · Standard · Sample paper, session 2023-24 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 8

From the official CBSE sample question paper for 2023-24, 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 ABC, DE AB. If AB = a, DE = x, BE = b and EC = c. Then x expressed in terms of a, b and c is:

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

Figure in the paper: Triangle ABC with A at top left, B at bottom left, C at bottom right. D lies on side AC and E lies on side BC, with DE parallel to AB. Labels: AB = a, DE = x, BE = b, EC = c. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

A line parallel to one side gives a smaller similar triangle.

Hint 2

. Compare DE with AB.

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 , (AA similarity: is common and corresponding angles are equal).

  2. So , which gives .

  3. Therefore . Option (B).

    1 mark

Answer: , option (B)

Where the marks are

  • Uses to get , 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 paperSample paper 2023-24 (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.