MathsCBSE Class 10 · Standard · Board exam 2025, set 30/1/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2025: question 34(a)

Set in the CBSE Class 10 board exam of 2025, paper 30/1/1, 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

The perimeter of a right triangle is 60 cm and its hypotenuse is 25 cm. Find the lengths of other two sides of the triangle.

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

Hints

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

Hint 1

Use the perimeter to find the sum of the two unknown sides.

Hint 2

Write one side in terms of the other and apply Pythagoras theorem with hypotenuse 25 cm.

Hint 3

You should get a quadratic. Find two numbers whose product is 300 and whose sum is 35.

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 other two sides be $x$ cm and $y$ cm.
From the perimeter: $x + y + 25 = 60$ .
1 mark
So $y = 35 - x$ .
½ mark
By Pythagoras theorem, $x^{2} + y^{2} = 2 5^{2}$ .
Substituting: $x^{2} + (35 - x)^{2} = 625$ .
1 mark
Expand: $x^{2} + 1225 - 70 x + x^{2} = 625$ , so $2 x^{2} - 70 x + 600 = 0$ .
Dividing by 2: $x^{2} - 35 x + 300 = 0$ .
1 mark
Factorise: $x^{2} - 20 x - 15 x + 300 = 0$ , so $(x - 20) (x - 15) = 0$ .
Therefore $x = 20$ or $x = 15$ .
1 mark
If $x = 20$ , then $y = 15$ . If $x = 15$ , then $y = 20$ .
Hence the other two sides are 15 cm and 20 cm.
Check: $15 + 20 + 25 = 60$ and $1 5^{2} + 2 0^{2} = 625 = 2 5^{2}$ .
½ mark

Answer: The other two sides are 15 cm and 20 cm.

Where the marks are

Writes the perimeter equation $x + y + 25 = 60$ (1 mark)
Expresses $y = 35 - x$ (½ mark)
Applies Pythagoras: $x^{2} + (35 - x)^{2} = 625$ (1 mark)
Simplifies to $x^{2} - 35 x + 300 = 0$ (1 mark)
Solves to get $x = 20$ or $15$ (1 mark)
States the sides as 15 cm and 20 cm (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 paper2025 board paper, set 30/1/1 (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 2025: question 34(a)

Hints

Step-by-step solution

Revise the chapter

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