if a farmer wants to make a fence for her chicks she only has 28 feet what is the area of the largest pen she can build

Question

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Answer 1

P=2l+2w

28=2l+2w

14=l+w

14-w=l

A=(14-w)*w

A=14w-w²

use -b/2a where b=14 and a=-1

-14/2(-1)=-14/-2=7

w=7 and l=7

A=7*7

A=49 square feet is the maximum area

the rectangle with the largest area will always be a square

using only arithmetic, 28/4=7 feet

if you used 6 feet and 8 feet, the area would be 6*8=48 square feet

5*9=45 square feet only

4*10=40 square feet only

and so on...

 

Answer 2

Sarah,

For the solution to make sense, the question should make sense. what is the shape of the pen?

For example,

for rectangle: you would use the area formula, A=bh.

1. In order for A to be the largest, you may assign values and plug it in to find the area. 
2. The length 28 is the perimeter: 28 = 2b + 2h, 14 = b + h
3. therefore, you may have values such as these pairs that add up to 14, as base and height: 1,13; 2,12; ... 6,8; and 7,7.
4. the largest area can be determined,

              A = 1(13), 2(12), ...6(8),  or 7(7)

              A = 13, 24,  ..., 48, 49

The largest area is 49 square feet.