related rates

Question

the sides of an equilateral triangle are increasing at a rate of 10cm/min. at what rate is this area of the triangle increasing when the sides are 30 cm long?

 

i ended up with 260cm^2/min which is different than my book so i am just wondering the steps and where i went wrong.

Answer 1

The area of an equilateral triangle is

 

A = (√(3)/4)x²

 

where  x is the side length of triangle.

 

Given:

x = 30

dx/dt = 10

 

You need to find dA/dt.

 

dA/dt = (dA / dx) * (dx / dt)

 

dA/dt = (√(3)/2)x * 10

dA/dt = (√(3) / 2) * 30 * 10

dA/dt = 150√3

 

dA/dt = 259.81 cm² / min

Answer 2

Hi Julia,

 

Are you using formula for area of equilateral triangle is A = s²√3/4?

If so, then dA/dt = 2s√3/4 ds/dt= s√3/2 ds/dt. 

 

Now try substituting given values into that equation.