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- anonymous

a building with a rectangular base is to be constructed on a lot in a form of a right triangle with legs 18m and 24m. if the building has one side along the hypotenuse of the triangle, find the dimensions of the base of the building for maximum floor area.

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- Kainui

First off, draw a picture.|dw:1328144793365:dw|
What are you trying to maximize? Area of the rectangle, which is simply a*b=A
Remember what a derivative does, it finds the slope of a line. When A is at its maximum value, it should look like a graph where A is the highest point. So when we find the derivative, we'll find that the derivative of that maximum point is equal to 0! Pretty nifty trick, yeah?
So that's the theory behind it, unfortunately the area isn't so simply a*b=A. You need to find out what the lengths of each sides are in relation to changing the length of one side. For example, you can already tell that if you make the side against the hypotenuse of the triangle longer, it'll flatten it out, and if you shorten it, you'll go the other way.

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