### The area of an equilateral plate, being heated, is increasing at a rate of 150 mm²/min. At what rate is the length of a side changing when the sides are 250 mm long?

Raw Transcript

Hello everyone. Tom from everystepcalculus.com and everystepphysics.com I’m going to do a test problem on an equilateral triangle with regards to related rates. Let’s see the problem is the area of an equilateral triangle plate being impeded is increasing at a rate 150 millimeters squared per minute. At what rate is the length of a side changing when the sides are 250 millimeters long? So, let’s do this. You have to put in index 8 open and close parentheses to get to my menu. And we’re going to scroll down to average rate of change. You could scroll to related rates. Let’s do that. They are both the same. And scroll down to the R section here. Here’s Related Rates there. And we’re going to hit number 7 for Equilateral Triangles. I’ll show you the formula here. Write this stuff on your paper. And of course you differentiate both sides with respect to time. What’s given here, they’re giving you the rate of change of the area so we’re going to go and enter the change. I’m going to press alpha to put anything in here. Alpha 150. And it gives millimeters. Choose number 2. And it gives minutes. Choose number 2. And then the side is Alpha 250. Now we’ll show you what you’ve entered so you can change it if you want. Say it’s okay. Write all this down.

Exactly as you see it. Here’s an answer. .69282 millimeters per minute. Pretty neat, huh.

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