MathsCBSE Class 10 · Basic · Board exam 2025, set 430/6/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 27

Set in the CBSE Class 10 board exam of 2025, paper 430/6/1, section C, question 27, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27 · 3 marks · Short answerCompetency-basedQuadratic Equations

Find length and breadth of a rectangular park whose perimeter is 100 m and area is $600 m^{2}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/6/1.

Hints

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

Hint 1

Write one equation from the perimeter and one from the area.

Hint 2

Substitute $b = 50 - a$ into the area equation and factorise the quadratic.

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.

Let length = $a$ m and breadth = $b$ m.
Perimeter: $2 (a + b) = 100 \Rightarrow a + b = 50$ …(i)
½ mark
Area: $ab = 600$ …(ii)
½ mark
From (i), $b = 50 - a$ . Substituting in (ii): $a (50 - a) = 600 \Rightarrow a^{2} - 50 a + 600 = 0$ .
1 mark
$(a - 30) (a - 20) = 0 \Rightarrow a = 30$ or $a = 20$ .
½ mark
Then $b = 20$ or $b = 30$ . So the length is 30 m and the breadth is 20 m.
½ mark

Answer: Length = 30 m, breadth = 20 m

Where the marks are

Forms $2 (a + b) = 100$ (½ mark)
Forms $ab = 600$ (½ mark)
Obtains quadratic $a^{2} - 50 a + 600 = 0$ (1 mark)
Solves to get $a = 30$ or $20$ (½ mark)
Gets corresponding breadth and states dimensions 30 m × 20 m (½ mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)

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 430/6/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 27

Hints

Step-by-step solution

Revise the chapter

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