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

CBSE Class 10 Mathematics Basic 2026: question 34(a)

Set in the CBSE Class 10 board exam of 2026, paper 430/5/1, section D, question 34(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34(a) · 5 marks · Long answerQuadratic Equations

ABCD is a rectangle of dimensions 80 cm $\times$ 60 cm. Another rectangle PQRS is drawn inside ABCD leaving space of equal width $x$ cm along the edges of ABCD. If area PQRS is half of the area ABCD, then find the value of $x$ .

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

The inner rectangle loses x cm at both ends of each side.

Hint 2

Set the inner area equal to half of $80 \times 60$ and solve the quadratic; check which root gives positive lengths.

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.

Leaving a strip of width $x$ cm on each side: $P Q = (80 - 2 x)$ cm, $QR = (60 - 2 x)$ cm.
2 marks
Area PQRS $= \frac{1}{2}$ Area ABCD $\Rightarrow (80 - 2 x) (60 - 2 x) = \frac{1}{2} \times 80 \times 60$ , i.e. $2 (80 - 2 x) (60 - 2 x) = 4800$
1 mark
$4800 - 280 x + 4 x^{2} = 2400 \Rightarrow 4 x^{2} - 280 x + 2400 = 0 \Rightarrow x^{2} - 70 x + 600 = 0$
1 mark
$(x - 10) (x - 60) = 0 \Rightarrow x = 10$ or $60$ . $x = 60$ is rejected since then $60 - 2 x < 0$ . So $x = 10$ cm.
1 mark

Answer: $x = 10$ cm

Where the marks are

Dimensions of PQRS: $80 - 2 x$ and $60 - 2 x$ (2 marks)
Forms equation from area condition (1 mark)
Gets $x^{2} - 70 x + 600 = 0$ (1 mark)
Solves and rejects 60; $x = 10$ cm (1 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 paper2026 board paper, set 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2026: question 34(a)

Hints

Step-by-step solution

Revise the chapter

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