MathsCBSE Class 10 · Standard · Board exam 2026, set 30/2/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2026: question 33(b)

Set in the CBSE Class 10 board exam of 2026, paper 30/2/1, section D, question 33(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33(b) · 5 marks · Long answerQuadratic Equations

The area of a right-angled triangle is $600 c m^{2}$ . If the base of the triangle exceeds the altitude by 10 cm, find all the three dimensions of the triangle.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/2/1.

Hints

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

Hint 1

Take the altitude as x; then the base is x + 10.

Hint 2

Use area = ½ × base × altitude, solve the quadratic, then use Pythagoras for the third side.

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 altitude be x cm, so base = (x + 10) cm. Area: $\frac{1}{2} \times x \times (x + 10) = 600$
1½ marks
$x^{2} + 10 x - 1200 = 0$
1 mark
$x^{2} + 40 x - 30 x - 1200 = 0 \Rightarrow (x + 40) (x - 30) = 0 \Rightarrow x = - 40$ or $x = 30$
1 mark
Length cannot be negative, so $x = 30$ ; altitude = 30 cm
½ mark
Base $= 30 + 10 = 40$ cm
½ mark
Hypotenuse $= 3 0^{2} + 4 0^{2} = 2500 = 50$ cm [Pythagoras theorem]
½ mark

Answer: Altitude = 30 cm, base = 40 cm, hypotenuse = 50 cm

Where the marks are

Forms $\frac{1}{2} x (x + 10) = 600$ (1½ marks)
Gets $x^{2} + 10 x - 1200 = 0$ (1 mark)
Factorises correctly (1 mark)
Altitude 30 cm, rejecting −40 (½ mark)
Base 40 cm (½ mark)
Hypotenuse 50 cm (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 paper2026 board paper, set 30/2/1 (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.

CBSE Class 10 Mathematics Standard 2026: question 33(b)

Hints

Step-by-step solution

Revise the chapter

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