# Thread: Related rates of change

1. ## Related rates of change

Hi there, I am asked this scenario:

The sides of an equilateral triangle are decreasing at a rate of da/dt=-(root6) cm. Find the rate of change of:

a) The area of the triangle
b) The height

I have drawn a diagram but I don't know how to go on about solving these problems

So i Know that for a) I'm meant to find da/dt
b) dh/dt

2. Originally Posted by notamaths_geniuszz
Hi there, I am asked this scenario:

The sides of an equilateral triangle are decreasing at a rate of da/dt=-(root6) cm. Find the rate of change of:

a) The area of the triangle
b) The height

I have drawn a diagram but I don't know how to go on about solving these problems

So i Know that for a) I'm meant to find da/dt
b) dh/dt

ok, first of all, what is the formula for the area and height in term of the side length?

Well the Area of a triangle is A=1/2*b*a
Three sides are the same so it is lets say: a
And the perpendicular height is lets say: h

A=1/2*a*h
I know it has something to do with pythagoras but I can't seem to get it after that.

4. Originally Posted by notamaths_geniuszz
Well the Area of a triangle is A=1/2*b*a
Three sides are the same so it is lets say: a
And the perpendicular height is lets say: h

A=1/2*a*h
I know it has something to do with pythagoras but I can't seem to get it after that.
Note that the area of an equilateral triangle is $A=\frac{\sqrt{3}}{4}s^2$, and the height of the triangle is defined as $h=\frac{\sqrt{3}}{2}s$, where s is the length of the side.

Can you take it from here?

--Chris

For a) A=root(3)/4 * s^2
So I'm trying to find Da/Dt
So the related rate of change is

dA/dt=DA/Da * Da/dt

Diff A=root(30)/4 * s^2 would give root(3)/2 *s

so this is what it would look like
DA/dt=root(3)/2 * s * -root(6)
So far is this right and how would i find that missing side length of s.

6. Originally Posted by notamaths_geniuszz
For a) A=root(3)/4 * s^2
So I'm trying to find Da/Dt
So the related rate of change is

dA/dt=DA/Da * Da/dt

Diff A=root(30)/4 * s^2 would give root(3)/2 *s

so this is what it would look like
DA/dt=root(3)/2 * s * -root(6)
So far is this right and how would i find that missing side length of s.
All of this looks right. I guess this would be the rate of change of the area, for any equilateral triangle with a side of length s [s is arbitrary].

--Chris