Triangle AreaDate: 05/24/99 at 11:22:18 From: Dermot Subject: Calculus A right triangle has a perimeter of 12m. Find the maximum area of the triangle. Date: 05/24/99 at 13:43:32 From: Doctor Jaffee Subject: Re: Calculus Hi Dermot, This problem looks a lot easier than it is, but I think I can help you solve it. Here is the outline of my solution. Let x and y be the lengths of the two legs of the triangle. Since the perimeter is 12, the length of the hypotenuse is 12 - (x + y). Furthermore, according to the Pythagorean theorem, x^2 + y^2 = [12 - (x + y)]^2 You can simplify this expression and solve for y in terms of x. Now, since area = (1/2)*base*height, substitute x for the base and your value of y in terms of x for the height. You want to maximize the area, so find the derivative dA/dx, set it equal to zero, and solve for x. You will find that x and y are the same, and if you multiply them together and divide by 2 you will have the maximum area. I hope this helps. Write back if you have any questions, or if my explanation needs more clarification. Good luck. - Doctor Jaffee, The Math Forum http://mathforum.org/dr.math/ |
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