SOLUTION: The perimeter of a rectangle is 100 feet. Let x represent the width of the rectangle and write a quadratic function that expressed the area of the rectangle in terms of its width.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The perimeter of a rectangle is 100 feet. Let x represent the width of the rectangle and write a quadratic function that expressed the area of the rectangle in terms of its width.      Log On


   

Question 118639: The perimeter of a rectangle is 100 feet. Let x represent the width of the rectangle and write a quadratic function that expressed the area of the rectangle in terms of its width.
Answer by ilana(307) About Me  (Show Source):
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This is tricky because we need to use perimeter to get area in terms of width. So, let's start with what we know. The perimeter is 100. The width is x. That means that out of the 4 sides of the rectangle, 2 are x. Or, you can think of it as one length and width (x) add to 50 (1/2 the perimeter). So length + x = 50.
Then length = 50 - x. So the area is length*width, or x*(50-x). As a quadratic function, Area=50x-x^2 or Area=-x^2+50x