Rates Question: An equilateral triangle is shrinking....

[peblez]

An Equilateral triangle is shrinking in such a way that it remains equilateral. At a particular time, the rate of change of the perimeter and the rate of change of the area are numerically equal. what is the value of perimeter at that instant.

this is what i did:

I found derivative of perimeter and the area.

Dp/dt = 3x
dp/dt = 3 (dx/dt)

da/dt = -3/4 x^2 (dx/dt ) - 3/8x^2 (dx/dt)

i combine both equations but turns out i get -8/3 = x^2 which is unsolveable

Please help

 

[tkhunny]

Why is the perimeter growing and the area shrinking? Shouldn't both be shrinking?

 

[peblez]

probably should, i think i made a mistake in the derivative of da/dt

 

[skeeter]

probably should, i think i made a mistake in the derivative of da/dt

\(\displaystyle \L A = \frac{\sqrt{3}}{4} x^2\)

\(\displaystyle \L \frac{dA}{dt} = \frac{\sqrt{3}}{2} x \frac{dx}{dt}\)

\(\displaystyle \L P = 3x\)

\(\displaystyle \L \frac{dP}{dt} = 3\frac{dx}{dt}\)

At a particular time, the rate of change of the perimeter and the rate of change of the area are numerically equal.

\(\displaystyle \L 3\frac{dx}{dt} = \frac{\sqrt{3}}{2} x \frac{dx}{dt}\)

solve for x ... then 3x = ?