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Case Study 1. A garden designer… (Class 10 Maths 2025, Q36)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/3/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2025: question 36

Set in the CBSE Class 10 board exam of 2025, paper 30/3/1, section E, question 36, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q36 · 4 marks · Case-basedCompetency-basedQuadratic Equations

Case Study 1. A garden designer is planning a rectangular lawn that is to be surrounded by a uniform walkway. The total area of the lawn and the walkway is 360 square metres. The width of the walkway is same on all sides. The dimensions of the lawn itself are 12 metres by 10 metres.

Based on the information given above, answer the following questions :

  1. (i)

    Formulate the quadratic equation representing the total area of the lawn and the walkway, taking width of walkway m.

    1 mark
  2. (ii)

    (a) Solve the quadratic equation to find the width of the walkway 'x'.

    2 marks

  3. OR

    (ii)

    (b) If the cost of paving the walkway at the rate of per square metre is , calculate the area of the walkway.

    2 marks
  4. (iii)

    Find the perimeter of the lawn.

    1 mark

Figure in the paper: A photograph of a rectangular green lawn surrounded by a stone walkway with plants around it, and a line diagram: a rectangle representing the lawn, labelled 10 m (vertical side) and 12 m (horizontal side), surrounded by a uniform walkway of width x on all sides, with x marked on the left and bottom edges. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/3/1.

Hints

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

Hint 1

The walkway adds on both sides, so each dimension of the lawn grows by .

Hint 2

Set the outer length × outer breadth equal to 360 and simplify. Solve by splitting the middle term, and remember a width must be positive.

Hint 3

For the cost part, area = cost ÷ rate per m².

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. (i) With the walkway of width m on every side, the outer rectangle measures m by m. So .

    ½ mark

  2. (i) Expanding: , i.e. , or .

    ½ mark

  3. (ii)(a) Splitting the middle term: .

    1 mark

  4. (ii)(a) This gives or . A width cannot be negative, so the width of the walkway is m.

    1 mark

  5. (ii)(b) Area of walkway

    1 mark

  6. (ii)(b) m. (Check: m.)

    1 mark

  7. (iii) Perimeter of the lawn m.

    1 mark

Answer: (i) ; (ii)(a) 4 m; (ii)(b) 240 m²; (iii) 44 m

Where the marks are

  • Writes (½ mark)
  • Simplifies to (½ mark)
  • (ii)(a) Factorises as (1 mark)
  • (ii)(a) Rejects the negative root and states the width as 4 m (1 mark)
  • (ii)(b) Divides the total cost by the rate, (1 mark)
  • (ii)(b) Gets the area as 240 m² (1 mark)
  • (iii) Perimeter m (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Quadratic Equations, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 30/3/1 (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.