Skip to content

The dimensions of a window are… (Class 10 Maths 2026, Q31)

questionbuddy.in/q/cbse-10-maths-2026-30-5-1-q31-dimensions-window-arjun-wants-put

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2026: question 31

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, section C, question 31, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31 · 3 marks · Short answerCompetency-basedReal Numbers

The dimensions of a window are 156 cm 216 cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/5/1.

Hints

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

Hint 1

The square's side must divide both 156 and 216 exactly.

Hint 2

Maximum size means the greatest common divisor — find the HCF by prime factorisation.

Hint 3

Divide the window area by the area of one square.

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. ½ mark

  2. ½ mark

  3. The largest square that fits exactly along both sides has side = HCF(156, 216) cm.

    1 mark

  4. Number of squares

    1 mark

Answer: Side of square = 12 cm; number of squares = 234

Where the marks are

  • Prime factorisation of 156 (½ mark)
  • Prime factorisation of 216 (½ mark)
  • Side = HCF = 12 cm (1 mark)
  • Number of squares = 234 (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Real Numbers, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/5/1 (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.