A charity trust decides to build a rectangular hall having an area of 300\ m². The length of the hall is one metre more than twice its width. Find the length and breadth of the hall.

MathsCBSE Class 10 · Basic · Board exam 2026, set 430/3/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2026: question 32(b)

Set in the CBSE Class 10 board exam of 2026, paper 430/3/1, section D, question 32(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(b) · 5 marks · Long answerQuadratic Equations

A charity trust decides to build a rectangular hall having an area of $300 m^{2}$ . The length of the hall is one metre more than twice its width. Find the length and breadth of the hall.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/3/1.

Hints

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

Hint 1

Let the breadth be x; write the length in terms of x.

Hint 2

Area = length × breadth gives a quadratic. Split the middle term using 25 and −24.

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 the breadth be $x$ m. Then the length is $(2 x + 1)$ m.
½ mark
Area $= 300$ : $x (2 x + 1) = 300$
1½ marks
$2 x^{2} + x - 300 = 0$
1½ marks
$2 x^{2} + 25 x - 24 x - 300 = 0 \Rightarrow x (2 x + 25) - 12 (2 x + 25) = 0 \Rightarrow (x - 12) (2 x + 25) = 0$
$x = 12$ or $x = - \frac{25}{2}$ . A breadth cannot be negative, so $x = 12$ .
1 mark
Breadth = 12 m and length = $2 (12) + 1 = 25$ m. Check: $25 \times 12 = 300 m^{2}$ .
½ mark

Answer: Length = 25 m, breadth = 12 m

Where the marks are

Takes breadth x and length 2x + 1 (½ mark)
Forms x(2x + 1) = 300 (1½ marks)
Writes the quadratic 2x² + x − 300 = 0 (1½ marks)
Solves and rejects the negative root to get x = 12 (1 mark)
States length 25 m and breadth 12 m (½ mark)

Revise the chapter

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

Practise this chapterBoard-style questions from Quadratic Equations, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 430/3/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2026: question 32(b)

Hints

Step-by-step solution

Revise the chapter

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