MathsCBSE Class 10 · Basic · Board exam 2026, set 430/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 25

Set in the CBSE Class 10 board exam of 2026, paper 430/5/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerTriangles

In the given figure, AB $∥$ DC. If OB = 3OD and CD = 1.8 cm, then find the length AB.

Figure in the paper: Two parallel horizontal lines: the upper line XY contains points D and C (D left, C right); the lower line X'Y' contains points A (left) and B (right). Segments AC and BD are drawn and intersect at O, which lies between the two lines. Given OB = 3OD and CD = 1.8 cm. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/5/1.

Hints

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

Hint 1

Look for two triangles with vertex O, one on each parallel line.

Hint 2

Use alternate angles to prove them similar, then compare OD/OB with CD/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.

In $△ O D C$ and $△ O B A$ : $∠ O D C = ∠ O B A$ and $∠ O C D = ∠ O A B$ [alternate angles, $D C ∥ A B$ ]. So $△ O D C \sim △ O B A$ (AA similarity).
½ mark
$\frac{O D}{O B} = \frac{C D}{A B}$ [corresponding sides of similar triangles]
½ mark
$O B = 3 O D \Rightarrow \frac{1}{3} = \frac{1.8}{A B}$
½ mark
$A B = 3 \times 1.8 = 5.4$ cm
½ mark

Answer: AB = 5.4 cm

Where the marks are

Proves $△ O C D \sim △ O A B$ by AA (½ mark)
Writes ratio of corresponding sides (½ mark)
Substitutes $\frac{1}{3} = \frac{1.8}{A B}$ (½ mark)
AB = 5.4 cm (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 430/5/1 (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.

CBSE Class 10 Mathematics Basic 2026: question 25

Hints

Step-by-step solution

Revise the chapter

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