Question

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?

Answer 1

Let a be the side of an equilateral triangle

Given:`(da)/(dt) = 3` cm/s

side a = 15

∴ Area of equilateral triangle = `(sqrt3  a^2)/4`

A = `(sqrt3 a^2)/4`

Differentiate w. r. t., t

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

= `sqrt3/4 xx 2 xx 15 xx 3`

= `(45sqrt3)/2  cm^2//sec`