Answer:
The dog pen is 12 square meters than the goat pen
Step-by-step explanation:
Area of the rectangular pen for the goats:
The perimeter of the pen is 20 meters. And a barn is used for one side length
so
L + 2B = 20
L = 20 -2B
[tex]Area = L\times B[/tex]
[tex]Area = (20-2B)\times B[/tex]
[tex]Area = (20B-2B^2)[/tex]
[tex]\frac{dA}{dB} = 20-4B[/tex]
20 -4B
20 = 4B
[tex]B=\frac{20}{4}[/tex]
B = 5
Now ,
L = 20-2B
L =20 -2(5)
L = 20 -10
L = 10
So area of the rectangular pen for goats
=> 10 x 5
=> 50 square metres
Area of the rectangular pen for the dogs:
The perimeter of the pen is 24 meters. And a barn is used for one side length
so
[tex]L' + 2B' = 24[/tex]
[tex]L' = L+2[/tex]
[tex]L' = 10+2[/tex]
[tex]L' = 12[/tex]
Now ,
[tex]12 + 2B' = 24[/tex]
[tex] 2B' = 24-12[/tex]
[tex] 2B' = 12[/tex]
[tex] B' = \frac{12}{2}[/tex]
[tex] B' =6[/tex]
Area of the rectangular pen for dogs
=>[tex]L' \times B'[/tex]
=> [tex]12 \times 6[/tex]
=> 72 square metres
Area of the rectangular pen for the goats - Area of the rectangular pen for the dogs
=>72 - 50
=> 12 square meters
