<p>OK I know this is for SAT preparation, but I have a very important mideast exam for calculus, and I know that since there are so many smart people on this website, one of you can answer this question! It is a calc I first-semester related rates question, so don't try to make it too confusing to read-thanks!</p>
<p>The sides of an equilateral triangle are increasing at the rate of 27 inches per second. How fast is the triangle's area increasing when the sides of the triangle are each 18 inches long?</p>
<p>So you have an equilateral triangle, so A=1/2bh You need the area formula in terms of either b or h. I’ll use b and then differentiate it.</p>
<p>Cut the triangle into two right triangles with a hypotenuse of b, a base of 0.5b and a height of h. Using the Pythagorean theorem find h in terms of b. You should get h = b*sqrt(3)/2</p>
<p>A = 0.5(sqrt(3)/2)*b^2 </p>
<p>Differentiate</p>
<p>dA/dt= (sqrt(3)/2)<em>b</em>db/dt</p>
<p>Plug in known values</p>
<p>dA/dt= (sqrt(3)/2)<em>18</em>27 = 243sqrt(3) in^2 per second</p>