The sum of areas of two squares is 2650 cm². If the sum of their perimeters is 280 cm, find the sides of the two given squares.

MathsCBSE Class 10 · Basic · Board exam 2026, set 430/2/1 · 5 marks · Long answer

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

Set in the CBSE Class 10 board exam of 2026, paper 430/2/1, section D, question 32(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(a) · 5 marks · Long answerQuadratic Equations

The sum of areas of two squares is $2650$ cm $^{2}$ . If the sum of their perimeters is $280$ cm, find the sides of the two given squares.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/2/1.

Hints

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

Hint 1

Let the sides be $x$ and $y$ ; the perimeter of a square is $4 \times$ side.

Hint 2

Use the perimeter equation to write $y$ in terms of $x$ .

Hint 3

Substitute into the area equation and solve the resulting 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 the sides of the two squares be $x$ cm and $y$ cm. Sum of perimeters: $4 x + 4 y = 280 \Rightarrow x + y = 70 \Rightarrow y = 70 - x$ .
1 mark
Sum of areas: $x^{2} + y^{2} = 2650 \Rightarrow x^{2} + (70 - x)^{2} = 2650$ .
1 mark
$2 x^{2} - 140 x + 4900 - 2650 = 0 \Rightarrow x^{2} - 70 x + 1125 = 0$ .
1 mark
Factorising: $(x - 45) (x - 25) = 0 \Rightarrow x = 45$ or $x = 25$ .
1 mark
If $x = 45$ then $y = 25$ ; if $x = 25$ then $y = 45$ . So the sides are 45 cm and 25 cm. Check: $4 5^{2} + 2 5^{2} = 2025 + 625 = 2650$ ✓.
1 mark

Answer: Sides are 45 cm and 25 cm

Where the marks are

Forms $x + y = 70$ from the perimeters (1 mark)
Forms $x^{2} + (70 - x)^{2} = 2650$ from the areas (1 mark)
Reduces it to $x^{2} - 70 x + 1125 = 0$ (1 mark)
Solves to get $x = 45$ or $25$ (1 mark)
States both sides, 45 cm and 25 cm (1 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 430/2/1 (Basic): every question, by section.

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

Hints

Step-by-step solution

Revise the chapter

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