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Lostsunrise [7]
3 years ago
6

A farmer has 100 m of fencing to enclose a rectangular pen. Which quadratic equation gives the area (A) of the pen, given its wi

dth (w)?
Mathematics
2 answers:
Nady [450]3 years ago
7 0

Answer:

A(w)=50w-w^2

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.

\text{Perimeter of rectangle}=2\text{ (Width+Length})

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

100=2(w\text{+Length})

\frac{100}{2}=\frac{2(w\text{+Length})}{2}

50=w\text{+Length}

50-w=w-w\text{+Length}

50-w=\text{Length}

\text{Area of rectangle}=\text{Width*Length}

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

\text{Area of rectangle}=w(50-w)

\text{Area of rectangle}=50w-w^2

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

A(w)=50w-w^2

Therefore, the area of our given pen will be A(w)=50w-w^2.

inn [45]3 years ago
5 0

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.

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