MathsCBSE Class 10 · Standard · Board exam 2026, set 30/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2026: question 22(A)

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, section B, question 22(A), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(A) · 2 marks · Very short answerTriangles

In $Δ$ ABC, DE $∥$ BC. If AD = $x$ , DB = $x - 2$ , AE = $x + 2$ and EC = $x - 1$ , then find the value of $x$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/1/1.

Hints

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

Hint 1

A line parallel to one side of a triangle divides the other two sides proportionally.

Hint 2

Cross-multiply; the $x^{2}$ 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.

Since DE ∥ BC, by the Basic Proportionality Theorem $\frac{A D}{D B} = \frac{A E}{E C}$ .
1 mark
$\frac{x}{x - 2} = \frac{x + 2}{x - 1}$ , so $x (x - 1) = (x - 2) (x + 2)$ , which gives $x^{2} - x = x^{2} - 4$ .
½ mark
$- x = - 4$ , so $x = 4$ .
½ mark

Answer: $x = 4$

Where the marks are

Applies BPT: AD/DB = AE/EC (1 mark)
Substitutes and cross-multiplies (½ mark)
Gets x = 4 (½ mark)

Revise the chapter

Chapter: Triangles (notes, formulas, where marks are lost and every past question)
Topic: Basic Proportionality Theorem (Thales Theorem)

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 30/1/1 (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.

CBSE Class 10 Mathematics Standard 2026: question 22(A)

Hints

Step-by-step solution

Revise the chapter

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