Question

A local farmer built a rectangular pen for her goats using 20 meters of fence. She used part of one side of her barn as one length of the rectangular pen. She maximized the area using 20 meters of fence. She then built a rectangular pen for her hogs using 24 meters of fence. She used part of one side of her barn as one length of the rectangular pen. The length of her pen was 2 meters more than the length of the goat pen. The width of her pen was 1 meter more than the width of the goat pen. How much larger is the hog pen than the goat pen?

Answer 1

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

$Area = L\times B$

$Area = (20-2B)\times B$

$Area = (20B-2B^2)$

$\frac{dA}{dB} = 20-4B$

20 -4B  

20 = 4B

$B=\frac{20}{4}$

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

$L' + 2B' = 24$

$L' = L+2$

$L' = 10+2$

$L' = 12$

Now ,

$12 + 2B' = 24$

$2B' = 24-12$

$2B' = 12$

$B' = \frac{12}{2}$

$B' =6$

Area of the rectangular pen for dogs

=>$L' \times B'$

=> $12 \times 6$

=> 72 square metres

Area of the rectangular pen for the goats - Area of the rectangular pen for the dogs

=>72 - 50

=> 12 square meters