Skip to content

ABC is a triangle in which DE… (Class 10 Maths 2023, Q25A)

questionbuddy.in/q/cbse-10-maths-2023-30-6-1-q25a-abc-triangle-value

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2023: question 25(A)

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, section B, question 25(A), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25(A) · 2 marks · Very short answerTriangles

In the given figure, ABC is a triangle in which DE BC. If AD = x, DB = x - 2, AE = x + 2 and EC = x - 1, then find the value of x.

Figure in the paper: Triangle ABC with apex A at top, B bottom-left, C bottom-right. D on AB and E on AC with DE parallel to BC. Labels: AD = x, DB = x − 2, AE = x + 2, EC = x − 1. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/6/1.

Hints

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

Hint 1

A line drawn parallel to one side of a triangle divides the other two sides in the same ratio.

Hint 2

Cross-multiply. The terms cancel.

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. In , DE ∥ BC, so by the Basic Proportionality Theorem .

    1 mark

  2. Cross-multiplying: , so , which gives .

    1 mark

Answer: x = 4

Where the marks are

  • Applies BPT to form (1 mark)
  • Solves to get x = 4 (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 paper2023 board paper, set 30/6/1 (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.