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The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when the side is 10 cm is
  • a)
    √3 sq. units/sec
  • b)
    10 sq. units/sec
  • c)
    10√3 sq. units/sec
  • d)
    10/√3 sq. units/sec
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The sides of an equilateral triangle are increasing at the rate of 2 c...
Given Information:
- Rate of increase of sides of equilateral triangle = 2 cm/sec
- Side length when area is to be calculated = 10 cm

Calculating the Area of Equilateral Triangle:
- The area of an equilateral triangle is given by the formula: Area = (√3/4) * side^2

Calculating the Rate of Change of Area:
- Differentiating the area formula with respect to time, we get: dA/dt = (√3/2) * side * (d(side)/dt)
- Substituting the given values, we get: dA/dt = (√3/2) * 10 * 2 = 10√3 sq. units/sec

Final Answer:
- Therefore, the rate at which the area increases when the side is 10 cm is 10√3 sq. units/sec, which corresponds to option 'C'.
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The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when the side is 10 cm isa)√3 sq. units/secb)10 sq. units/secc)10√3 sq. units/secd)10/√3 sq. units/secCorrect answer is option 'C'. Can you explain this answer?
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The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when the side is 10 cm isa)√3 sq. units/secb)10 sq. units/secc)10√3 sq. units/secd)10/√3 sq. units/secCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when the side is 10 cm isa)√3 sq. units/secb)10 sq. units/secc)10√3 sq. units/secd)10/√3 sq. units/secCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when the side is 10 cm isa)√3 sq. units/secb)10 sq. units/secc)10√3 sq. units/secd)10/√3 sq. units/secCorrect answer is option 'C'. Can you explain this answer?.
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