Respuesta :
The pig pen is 14 sq. meters larger than the chicken pen built by the former.
What are the perimeter and area of a rectangle?
Consider a rectangle with length 'L' and width 'W'.
So, its perimeter = 2(L + W) units and area = L × W sq. units.
Calculating the dimensions of the rectangular pen for chicken:
It is given that a farmer built a rectangular pen for chickens.
The chicken pen's perimeter is 12 meters, and she used only one side of the barn as one length of the rectangular pen.
So,
L + 2W = 12
⇒ L = 12 - 2W
Then its area is calculated as below:
Area = L × W
= (12 - 2W) W
= 12W - 2W²
Consider A' = 0 for finding the larger area.
So, differentiating the area w.r.t W,
dA/dW = 12 - 4W
0 = 12 - 4W
⇒ 4W = 12
∴W = 3 meters
Then,
L = 12 - 2W = 12 - 2(3) = 6 meters
So, the area of the chicken pen = 6m × 3m = 18 m²
Calculating the dimensions of the rectangular pen for the pig:
It is given that,
The length of the pig pen was 2 meters more than the length of the chicken pen. I.e., L' = L + 2
The width of the pig pen was 1 meter more than the width of the chicken pen. I.e., W' = W + 1
On substituting L and W values to find the dimensions of the pig pen,
L' = 6 + 2 = 8m
W' = 3 + 1 = 4m
Then,
Area = L' × W'
= 8m × 4m
= 32 m²
Finding how much larger is the pig pen than the chicken pen:
Area of the pig pen - Area of the chicken pen
⇒ 32 m² - 18 m² = 14 m²
Therefore, the pig pen is 14 m² larger than the chicken pen.
Refer similar problem here:
https://brainly.com/question/14323542
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