Afarmer has 100 m of fencing to enclose a rectangular pen. which quadratic equation gives the area (a) of the pen, given its width (w)?

A(w)=50w-w2 if the perimeter is 100, I plugged in possible values for the width...I used w=15 and length = 35 for a perimeter of 100. then I plugged these values in the possible equations until I found the correct one giving me an area of 525 (15x35) . I could not think of an easier way.

Step-by-step explanation:

Let w be the width of rectangular pen.

We have been given that a framer has 100 m of fencing to enclose a rectangular pen. This means that perimeter of pen is 100 meter.

Since the perimeter is 2 times the length and width of rectangle.

Upon substituting our given values in above formula we will get,

Upon substituting our given values in area formula we will get,

Let us represent area in terms of width of rectangle as:

Therefore, the area of our given pen will be .

rounding to the nearest thousandth would be 452,000

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