MathsCBSE Class 12 · Board exam 2025, set 65/1/1 · 3 marks · Short answer

CBSE Class 12 Mathematics 2025: question 26

Set in the CBSE Class 12 board exam of 2025, paper 65/1/1, section C, question 26, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26 · 3 marks · Short answerApplication of Derivatives

The side of an equilateral triangle is increasing at the rate of 3 cm/s. At what rate its area increasing when the side of the triangle is 15 cm ?

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 65/1/1.

Hints

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

Hint 1

Write the area of an equilateral triangle in terms of its side.

Hint 2

Differentiate the area with respect to time using the chain rule, then put $a = 15$ and $\frac{d a}{d t} = 3$ .

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 $a$ be the side of the triangle. Then $\frac{d a}{d t} = 3$ cm/s.
½ mark
Area of an equilateral triangle: $A = \frac{3}{4} a^{2}$ . Differentiating with respect to $t$ : $\frac{d A}{d t} = \frac{3}{2} a \frac{d a}{d t}$ .
1½ marks
At $a = 15$ cm: $\frac{d A}{d t} = \frac{3 \times 15}{2} \times 3 = \frac{45 3}{2}$ cm²/s.
1 mark

Answer: The area is increasing at $\frac{45 3}{2}$ cm²/s

Where the marks are

Writes $\frac{d a}{d t} = 3$ cm/s (½ mark)
Uses $A = \frac{3}{4} a^{2}$ and gets $\frac{d A}{d t} = \frac{3}{2} a \frac{d a}{d t}$ (1½ marks)
Substitutes to get $\frac{45 3}{2}$ cm²/s (1 mark)

Revise the chapter

Chapter: Application of Derivatives (notes, formulas, where marks are lost and every past question)
Topic: Rate of Change of Quantities

Practise this chapterBoard-style questions from Application of Derivatives, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 65/1/1: every question, by section.

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CBSE Class 12 Mathematics 2025: question 26

Hints

Step-by-step solution

Revise the chapter

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