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# The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm ? - CBSE (Commerce) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm ?

#### Solution

Area of an equilateral triangle, A = sqrt3/4 a^2

where

a = Side of an equilateral triangle

Given:

(da)/(dt) =2 cm/s

Now,

(dA)/(dt)=d/dt(sqrt3/4a^2)

=sqrt3/4 xx 2 xx a xx(da)/(dt)

=(sqrt3a)/2xx(da)/(dt)

=(sqrt3a)/2xx2

=sqrt3a cm2/s

therefore [(dA)/(dt)]_(a=20)=20sqrt3 cm2/s

Hence, the area is increasing at the rate of 20sqrt3 cm2/s when the side of the triangle is 20 cm.

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Solution The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm ? Concept: Increasing and Decreasing Functions.
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