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cluelezz123 · Oct 7, 2008, 09:51 PM

Hi there,

I am given a scenario stating that

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

cluelezz123 · Oct 7, 2008, 10:11 PM

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

But I don't know to do arrive at the answer... please help.

cluelezz123 · Oct 8, 2008, 03:55 AM

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.

Unknown008 · Oct 9, 2008, 12:30 AM

You're using 'a', now 's'... i think that you're confusing yourself. If i understood well what you meant, then, this is an equilateral triangle and all the sides are equal so a=s.

Use the formula:

$\frac{dA}{dt}=\frac{dA}{dh}\times\frac{dh}{dt}$

To find dA/dh, use the other formula for area of triangle,

$A = \frac{1}{2} base \times height$

Now you need a formula linking a and h. When you find that, substitute a in the formula of the area of the triangle and differentiate to have dA/dh.

Hope it helped.

galactus · Oct 10, 2008, 09:03 AM

The area of an equilateral triangle is given by $A=\frac{\sqrt{3}}{4}s^{2}$ , where s is the length of a side.

Differentiate:

$\frac{dA}{dt}=\frac{\sqrt{3}}{2}s\cdot \frac{ds}{dt}$

You are given ds/dt, plug it in.

The height of an equilateral is given by $h=\frac{\sqrt{3}}{2}s$

Do the same thing as above.

Unknown008 · Oct 11, 2008, 02:12 AM

In other words, that's neraly the same as what I said...

galactus · Oct 11, 2008, 05:16 AM

I'm sorry, I reckon you did. My apologies.